\(x^2+9x+20\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2+9x+20\)?
#factorisation
#quadratic
#algebraic identities
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A ( (x+2)(x+10) )
B ( (x+4)(x+5) )
C ( (x-4)(x-5) )
D ( (x+1)(x+20) )
Explanation opens after your attempt
Correct Answer
B. ( (x+4)(x+5) )
Step 1
Concept
The numbers (4) and (5) have sum (9) and product (20). Exam tip: check both sum and product while splitting the middle term.
Step 2
Why this answer is correct
The correct answer is B. ( (x+4)(x+5) ). The numbers (4) and (5) have sum (9) and product (20). Exam tip: check both sum and product while splitting the middle term.
Step 3
Exam Tip
(4) और (5) का योग (9) और गुणनफल (20) है। परीक्षा में मध्य पद तोड़ते समय योग और गुणनफल दोनों जांचें।
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\(a^2-16\) को गुणनखंडों में लिखिए।
Write \(a^2-16\) in factors.
#difference of squares
#factorisation
#identity
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A ( (a-4)(a+4) )
B ( (a-8)(a+2) )
C ( (a+4)(a+4) )
D ( (a-2)(a+8) )
Explanation opens after your attempt
Correct Answer
A. ( (a-4)(a+4) )
Step 1
Concept
It is \(a^2-4^2\) so the difference of squares identity applies. Exam tip: remember (p-2 -q-2 =(p-q)(p+q)).
Step 2
Why this answer is correct
The correct answer is A. ( (a-4)(a+4) ). It is \(a^2-4^2\) so the difference of squares identity applies. Exam tip: remember (p-2 -q-2 =(p-q)(p+q)).
Step 3
Exam Tip
यह \(a^2-4^2\) है इसलिए अंतर वर्ग पहचान लागू होगी। परीक्षा में (p-2 -q-2 =(p-q)(p+q)) याद रखें।
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\(y^2-12y+36\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(y^2-12y+36\)?
#perfect square
#trinomial
#factorisation
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A ( (y+6)2 )
B ( (y-4)(y-9) )
C ( (y-6)2 )
D ( (y-3)(y-12) )
Explanation opens after your attempt
Correct Answer
C. ( (y-6)2 )
Step 1
Concept
It is \(y^2-2\cdot y\cdot6+6^2\). Exam tip: identify perfect square trinomials first.
Step 2
Why this answer is correct
The correct answer is C. ( (y-6)2 ). It is \(y^2-2\cdot y\cdot6+6^2\). Exam tip: identify perfect square trinomials first.
Step 3
Exam Tip
यह \(y^2-2\cdot y\cdot6+6^2\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचान को पहले पहचानें।
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\(m^2+11m+30\) के गुणनखंड क्या हैं?
What are the factors of \(m^2+11m+30\)?
#quadratic
#factorisation
#middle term
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A ( (m+3)(m+8) )
B ( (m+4)(m+7) )
C ( (m-5 )(m-6 ) )
D ( (m+5)(m+6) )
Explanation opens after your attempt
Correct Answer
D. ( (m+5)(m+6) )
Step 1
Concept
The numbers (5) and (6) have sum (11) and product (30). Exam tip: for a positive middle term choose signs carefully.
Step 2
Why this answer is correct
The correct answer is D. ( (m+5)(m+6) ). The numbers (5) and (6) have sum (11) and product (30). Exam tip: for a positive middle term choose signs carefully.
Step 3
Exam Tip
(5) और (6) का योग (11) और गुणनफल (30) है। परीक्षा में धनात्मक मध्य पद के लिए दोनों गुणनखंडों के चिन्ह ध्यान से लें।
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\(p^2-25q^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(p^2-25q^2\).
#difference of squares
#binomial
#factorisation
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A ( (p-5q)(p+5q) )
B ( (p-25q)(p+q) )
C ( (p+5q)2 )
D ( (p-5q)2 )
Explanation opens after your attempt
Correct Answer
A. ( (p-5q)(p+5q) )
Step 1
Concept
Writing \(25q^2\) as ((5q)2 ) gives the difference of squares identity. Exam tip: first see both terms as squares.
Step 2
Why this answer is correct
The correct answer is A. ( (p-5q)(p+5q) ). Writing \(25q^2\) as ((5q)2 ) gives the difference of squares identity. Exam tip: first see both terms as squares.
Step 3
Exam Tip
\(25q^2\) को ((5q)2 ) लिखने पर अंतर वर्ग पहचान मिलती है। परीक्षा में पहले दोनों पदों को वर्ग के रूप में देखें।
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\(x^2-7x+10\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(x^2-7x+10\)?
#quadratic
#negative middle term
#factorisation
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A ( (x-1)(x-10) )
B ( (x-2)(x-5) )
C ( (x+2)(x+5) )
D ( (x-3)(x-4) )
Explanation opens after your attempt
Correct Answer
B. ( (x-2)(x-5) )
Step 1
Concept
The numbers (-2) and (-5) have sum (-7) and product (10). Exam tip: a negative middle term may need both negative signs.
Step 2
Why this answer is correct
The correct answer is B. ( (x-2)(x-5) ). The numbers (-2) and (-5) have sum (-7) and product (10). Exam tip: a negative middle term may need both negative signs.
Step 3
Exam Tip
(-2) और (-5) का योग (-7) और गुणनफल (10) है। परीक्षा में ऋणात्मक मध्य पद में दोनों ऋण चिन्ह लग सकते हैं।
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\(4r^2-81\) को गुणनखंडों में लिखिए।
Write \(4r^2-81\) in factors.
#identity
#difference of squares
#factorisation
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A ( (2r-9)(2r+9) )
B ( (4r-9)(r+9) )
C ( (2r+9)2 )
D ( (r-9)(4r+9) )
Explanation opens after your attempt
Correct Answer
A. ( (2r-9)(2r+9) )
Step 1
Concept
Here (4r-2 =(2r)2 ) and \(81=9^2\). Exam tip: identify squares and apply \(p^2-q^2\) quickly.
Step 2
Why this answer is correct
The correct answer is A. ( (2r-9)(2r+9) ). Here (4r-2 =(2r)2 ) and \(81=9^2\). Exam tip: identify squares and apply \(p^2-q^2\) quickly.
Step 3
Exam Tip
(4r-2 =(2r)2 ) और \(81=9^2\) हैं। परीक्षा में वर्ग पहचानकर तुरंत \(p^2-q^2\) लगाएं।
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\(z^2+14z+49\) का गुणनखंड रूप क्या है?
What is the factorised form of \(z^2+14z+49\)?
#perfect square
#algebraic identity
#factorisation
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A ( (z+14)(z+1) )
B ( (z-7)2 )
C ( (z+7)2 )
D ( (z+5)(z+9) )
Explanation opens after your attempt
Correct Answer
C. ( (z+7)2 )
Step 1
Concept
It is \(z^2+2\cdot z\cdot7+7^2\). Exam tip: recognise the ((a+b)2 ) identity.
Step 2
Why this answer is correct
The correct answer is C. ( (z+7)2 ). It is \(z^2+2\cdot z\cdot7+7^2\). Exam tip: recognise the ((a+b)2 ) identity.
Step 3
Exam Tip
यह \(z^2+2\cdot z\cdot7+7^2\) है। परीक्षा में ((a+b)2 ) की पहचान करें।
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\(6x^2+15x\) में सार्व गुणनखंड निकालकर सही रूप चुनिए।
Choose the correct form of \(6x^2+15x\) after taking out the common factor.
#common factor
#monomial
#factorisation
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A (3x(2x+5))
B (3(2x+5))
C (x(6x+15))
D (5x(2x+3))
Explanation opens after your attempt
Correct Answer
A. (3x(2x+5))
Step 1
Concept
Both terms have (3x) as the common factor. Exam tip: first take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (3x(2x+5)). Both terms have (3x) as the common factor. Exam tip: first take out the greatest common factor.
Step 3
Exam Tip
दोनों पदों में (3x) सार्व गुणनखंड है। परीक्षा में पहले सबसे बड़ा सार्व गुणनखंड निकालें।
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(ab+ac+db+dc) का समूह बनाकर गुणनखंड क्या होगा?
What is the factorisation of (ab+ac+db+dc) by grouping?
#grouping
#factorisation
#common binomial
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A ( (a+d)(b+c) )
B ( (a+b)(c+d) )
C ( (a+c)(b+d) )
D ( (a-d)(b-c) )
Explanation opens after your attempt
Correct Answer
A. ( (a+d)(b+c) )
Step 1
Concept
Taking (a) from the first two terms and (d) from the last two gives common (b+c). Exam tip: aim to create a common binomial.
Step 2
Why this answer is correct
The correct answer is A. ( (a+d)(b+c) ). Taking (a) from the first two terms and (d) from the last two gives common (b+c). Exam tip: aim to create a common binomial.
Step 3
Exam Tip
पहले दो पदों से (a) और अंतिम दो से (d) निकालने पर (b+c) समान आता है। परीक्षा में समान द्विपद बनाना लक्ष्य रखें।
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\(x^2-49y^2\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2-49y^2\)?
#difference of squares
#factorisation
#binomial
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A ( (x-7y)(x+7y) )
B ( (x-49y)(x+y) )
C ( (x+7y)(x+7y) )
D ( (x-7y)(x-7y) )
Explanation opens after your attempt
Correct Answer
A. ( (x-7y)(x+7y) )
Step 1
Concept
Since (49y-2 =(7y)2 ), the difference of squares identity applies. Exam tip: spot forms like \(x^2-a^2\) quickly.
Step 2
Why this answer is correct
The correct answer is A. ( (x-7y)(x+7y) ). Since (49y-2 =(7y)2 ), the difference of squares identity applies. Exam tip: spot forms like \(x^2-a^2\) quickly.
Step 3
Exam Tip
(49y-2 =(7y)2 ) है इसलिए अंतर वर्ग पहचान लगेगी। परीक्षा में \(x^2-a^2\) जैसे रूप तुरंत पहचानें।
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\(n^2-3n-28\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(n^2-3n-28\)?
#quadratic
#middle term
#signs
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A ( (n-7)(n+4) )
B ( (n+7)(n-4) )
C ( (n-14)(n+2) )
D ( (n-1)(n-28) )
Explanation opens after your attempt
Correct Answer
A. ( (n-7)(n+4) )
Step 1
Concept
The numbers (-7) and (4) have sum (-3) and product (-28). Exam tip: negative product means opposite signs.
Step 2
Why this answer is correct
The correct answer is A. ( (n-7)(n+4) ). The numbers (-7) and (4) have sum (-3) and product (-28). Exam tip: negative product means opposite signs.
Step 3
Exam Tip
(-7) और (4) का योग (-3) और गुणनफल (-28) है। परीक्षा में ऋणात्मक गुणनफल में चिन्ह अलग अलग होते हैं।
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\(9a^2+24a+16\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(9a^2+24a+16\).
#perfect square trinomial
#identity
#factorisation
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A ( (3a+4)2 )
B ( (3a-4)2 )
C ( (9a+4)(a+4) )
D ( (3a+8)(3a+2) )
Explanation opens after your attempt
Correct Answer
A. ( (3a+4)2 )
Step 1
Concept
It is ((3a)2 +2\cdot3a\cdot4+42 ). Exam tip: when first and last terms are squares, check the middle term.
Step 2
Why this answer is correct
The correct answer is A. ( (3a+4)2 ). It is ((3a)2 +2\cdot3a\cdot4+42 ). Exam tip: when first and last terms are squares, check the middle term.
Step 3
Exam Tip
यह ((3a)2 +2\cdot3a\cdot4+42 ) है। परीक्षा में पहला और अंतिम पद वर्ग हों तो मध्य पद जांचें।
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(2xy+6x+5y+15) का गुणनखंड क्या है?
What is the factorisation of (2xy+6x+5y+15)?
#grouping
#factorisation
#common binomial
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A ( (2x+5)(y+3) )
B ( (2x+3)(y+5) )
C ( (x+5)(2y+3) )
D ( (2x-5)(y-3) )
Explanation opens after your attempt
Correct Answer
A. ( (2x+5)(y+3) )
Step 1
Concept
Grouping gives (2x(y+3)+5(y+3)). Exam tip: group terms until a common bracket appears.
Step 2
Why this answer is correct
The correct answer is A. ( (2x+5)(y+3) ). Grouping gives (2x(y+3)+5(y+3)). Exam tip: group terms until a common bracket appears.
Step 3
Exam Tip
समूह बनाने पर (2x(y+3)+5(y+3)) मिलता है। परीक्षा में समान ब्रैकेट बनने तक पदों को सही समूह में रखें।
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\(16u^2-24uv+9v^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(16u^2-24uv+9v^2\)?
#perfect square
#negative middle term
#factorisation
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A ( (4u+3v)2 )
B ( (4u-3v)2 )
C ( (16u-9v)2 )
D ( (4u-9v)(4u+v) )
Explanation opens after your attempt
Correct Answer
B. ( (4u-3v)2 )
Step 1
Concept
It is ((4u)2 -2\cdot4u\cdot3v+(3v)2 ). Exam tip: for a negative middle term, check ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is B. ( (4u-3v)2 ). It is ((4u)2 -2\cdot4u\cdot3v+(3v)2 ). Exam tip: for a negative middle term, check ((a-b)2 ).
Step 3
Exam Tip
यह ((4u)2 -2\cdot4u\cdot3v+(3v)2 ) है। परीक्षा में ऋणात्मक मध्य पद हो तो ((a-b)2 ) देखें।
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\(s^2-2s-35\) को गुणनखंडों में लिखिए।
Write \(s^2-2s-35\) in factors.
#quadratic
#factorisation
#sign choice
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A ( (s+7)(s-5 ) )
B ( (s-7 )(s+5) )
C ( (s-1 )(s-35 ) )
D ( (s+35)(s-1 ) )
Explanation opens after your attempt
Correct Answer
B. ( (s-7 )(s+5) )
Step 1
Concept
The numbers (-7) and (5) have sum (-2) and product (-35). Exam tip: the sign of the larger magnitude decides the middle term sign.
Step 2
Why this answer is correct
The correct answer is B. ( (s-7 )(s+5) ). The numbers (-7) and (5) have sum (-2) and product (-35). Exam tip: the sign of the larger magnitude decides the middle term sign.
Step 3
Exam Tip
(-7) और (5) का योग (-2) और गुणनफल (-35) है। परीक्षा में बड़े परिमाण वाले पद का चिन्ह मध्य पद तय करता है।
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\(27x^3+8y^3\) का गुणनखंड रूप क्या है?
What is the factorised form of \(27x^3+8y^3\)?
#sum of cubes
#factorisation
#identity
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A ( (3x+2y)\(9x^2-6xy+4y^2\) )
B ( (3x-2y)\(9x^2+6xy+4y^2\) )
C ( (3x+2y)\(9x^2+6xy+4y^2\) )
D ( (27x+8y)\(x^2-y^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (3x+2y)\(9x^2-6xy+4y^2\) )
Step 1
Concept
It is ((3x)3 +(2y)3 ). Exam tip: remember signs in (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)).
Step 2
Why this answer is correct
The correct answer is A. ( (3x+2y)\(9x^2-6xy+4y^2\) ). It is ((3x)3 +(2y)3 ). Exam tip: remember signs in (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)).
Step 3
Exam Tip
यह ((3x)3 +(2y)3 ) है। परीक्षा में (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)) का चिन्ह ध्यान रखें।
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\(8p^3-125q^3\) के गुणनखंड चुनिए।
Choose the factors of \(8p^3-125q^3\).
#difference of cubes
#factorisation
#identity
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A ( (2p+5q)\(4p^2-10pq+25q^2\) )
B ( (2p-5q)\(4p^2+10pq+25q^2\) )
C ( (2p-5q)\(4p^2-10pq+25q^2\) )
D ( (8p-125q)\(p^2+pq+q^2\) )
Explanation opens after your attempt
Correct Answer
B. ( (2p-5q)\(4p^2+10pq+25q^2\) )
Step 1
Concept
It is ((2p)3 -(5q)3 ). Exam tip: remember (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)).
Step 2
Why this answer is correct
The correct answer is B. ( (2p-5q)\(4p^2+10pq+25q^2\) ). It is ((2p)3 -(5q)3 ). Exam tip: remember (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)).
Step 3
Exam Tip
यह ((2p)3 -(5q)3 ) है। परीक्षा में (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)) याद रखें।
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\(x^2+2xy+y^2-25\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(x^2+2xy+y^2-25\)?
#mixed identity
#difference of squares
#factorisation
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A ( (x+y-5)(x+y+5) )
B ( (x-y-5)(x-y+5) )
C ( (x+y-25)(x+y+1) )
D ( (x+y)2 +25 )
Explanation opens after your attempt
Correct Answer
A. ( (x+y-5)(x+y+5) )
Step 1
Concept
First write \(x^2+2xy+y^2\) as ((x+y)2 ). Exam tip: solve mixed identities in two steps.
Step 2
Why this answer is correct
The correct answer is A. ( (x+y-5)(x+y+5) ). First write \(x^2+2xy+y^2\) as ((x+y)2 ). Exam tip: solve mixed identities in two steps.
Step 3
Exam Tip
पहले \(x^2+2xy+y^2\) को ((x+y)2 ) बनाएं। परीक्षा में मिश्रित पहचान को दो चरणों में हल करें।
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\(4x^2+12x+9-y^2\) के गुणनखंड क्या होंगे?
What will be the factors of \(4x^2+12x+9-y^2\)?
#perfect square
#difference of squares
#factorisation
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A ( (2x+3-y)(2x+3+y) )
B ( (2x-3-y)(2x-3+y) )
C ( (4x+9-y)(x+1+y) )
D ( (2x+y+3)2 )
Explanation opens after your attempt
Correct Answer
A. ( (2x+3-y)(2x+3+y) )
Step 1
Concept
Write \(4x^2+12x+9\) as ((2x+3)2 ) and then use difference of squares. Exam tip: forming a perfect square first is useful.
Step 2
Why this answer is correct
The correct answer is A. ( (2x+3-y)(2x+3+y) ). Write \(4x^2+12x+9\) as ((2x+3)2 ) and then use difference of squares. Exam tip: forming a perfect square first is useful.
Step 3
Exam Tip
\(4x^2+12x+9\) को ((2x+3)2 ) लिखकर अंतर वर्ग लगाएं। परीक्षा में पहले पूर्ण वर्ग बनाना उपयोगी होता है।
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\(3a^2+12ab\) का सार्व गुणनखंड निकालकर रूप क्या है?
What is the form of \(3a^2+12ab\) after taking the common factor?
#common factor
#monomial
#factorisation
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A (3a(a+4b))
B (3\(a^2+4ab\))
C (a(3a+12b))
D (6a(a+2b))
Explanation opens after your attempt
Correct Answer
A. (3a(a+4b))
Step 1
Concept
The greatest common factor of both terms is (3a). Exam tip: avoid taking an incomplete common factor.
Step 2
Why this answer is correct
The correct answer is A. (3a(a+4b)). The greatest common factor of both terms is (3a). Exam tip: avoid taking an incomplete common factor.
Step 3
Exam Tip
दोनों पदों में सबसे बड़ा सार्व गुणनखंड (3a) है। परीक्षा में अधूरा सार्व गुणनखंड निकालने से बचें।
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\(x^2-13x+42\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(x^2-13x+42\)?
#quadratic
#factorisation
#signs
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A ( (x-6)(x-7) )
B ( (x+6)(x+7) )
C ( (x-3)(x-14) )
D ( (x-2)(x-21) )
Explanation opens after your attempt
Correct Answer
A. ( (x-6)(x-7) )
Step 1
Concept
The numbers (-6) and (-7) have sum (-13) and product (42). Exam tip: if the constant is positive and the middle term is negative, both signs may be negative.
Step 2
Why this answer is correct
The correct answer is A. ( (x-6)(x-7) ). The numbers (-6) and (-7) have sum (-13) and product (42). Exam tip: if the constant is positive and the middle term is negative, both signs may be negative.
Step 3
Exam Tip
(-6) और (-7) का योग (-13) और गुणनफल (42) है। परीक्षा में अंतिम पद धनात्मक और मध्य पद ऋणात्मक हो तो दोनों चिन्ह ऋण हो सकते हैं।
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(5mn-10m+3n-6) का गुणनखंड रूप क्या है?
What is the factorised form of (5mn-10m+3n-6)?
#grouping
#common binomial
#factorisation
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A ( (5m+3)(n-2) )
B ( (5m-3)(n+2) )
C ( (m+3)(5n-2) )
D ( (5m+6)(n-1) )
Explanation opens after your attempt
Correct Answer
A. ( (5m+3)(n-2) )
Step 1
Concept
Grouping gives (5m(n-2)+3(n-2)). Exam tip: arrange terms so that a common bracket appears.
Step 2
Why this answer is correct
The correct answer is A. ( (5m+3)(n-2) ). Grouping gives (5m(n-2)+3(n-2)). Exam tip: arrange terms so that a common bracket appears.
Step 3
Exam Tip
समूह बनाने पर (5m(n-2)+3(n-2)) मिलता है। परीक्षा में पदों को इस तरह सजाएं कि समान ब्रैकेट निकले।
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\(25x^2-30xy+9y^2\) के गुणनखंड क्या हैं?
What are the factors of \(25x^2-30xy+9y^2\)?
#perfect square trinomial
#factorisation
#identity
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A ( (5x-3y)2 )
B ( (5x+3y)2 )
C ( (25x-9y)2 )
D ( (5x-9y)(5x+y) )
Explanation opens after your attempt
Correct Answer
A. ( (5x-3y)2 )
Step 1
Concept
It is ((5x)2 -2\cdot5x\cdot3y+(3y)2 ). Exam tip: match the middle term with (2ab).
Step 2
Why this answer is correct
The correct answer is A. ( (5x-3y)2 ). It is ((5x)2 -2\cdot5x\cdot3y+(3y)2 ). Exam tip: match the middle term with (2ab).
Step 3
Exam Tip
यह ((5x)2 -2\cdot5x\cdot3y+(3y)2 ) है। परीक्षा में मध्य पद को (2ab) से मिलाएं।
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\(q^2+q-56\) को गुणनखंडों में बदलें।
Convert \(q^2+q-56\) into factors.
#quadratic
#factorisation
#middle term
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A ( (q+8)(q-7) )
B ( (q-8)(q+7) )
C ( (q+4)(q-14) )
D ( (q-1)(q+56) )
Explanation opens after your attempt
Correct Answer
A. ( (q+8)(q-7) )
Step 1
Concept
The numbers (8) and (-7) have sum (1) and product (-56). Exam tip: even when the coefficient of (q) is (1), do not skip middle-term checking.
Step 2
Why this answer is correct
The correct answer is A. ( (q+8)(q-7) ). The numbers (8) and (-7) have sum (1) and product (-56). Exam tip: even when the coefficient of (q) is (1), do not skip middle-term checking.
Step 3
Exam Tip
(8) और (-7) का योग (1) और गुणनफल (-56) है। परीक्षा में (q) का गुणांक (1) हो तब भी मध्य पद को न छोड़ें।
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\(a^3+64\) का गुणनखंड रूप क्या है?
What is the factorised form of \(a^3+64\)?
#sum of cubes
#identity
#factorisation
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A ( (a+4)\(a^2-4a+16\) )
B ( (a-4)\(a^2+4a+16\) )
C ( (a+4)\(a^2+4a+16\) )
D ( (a+8)\(a^2-8a+64\) )
Explanation opens after your attempt
Correct Answer
A. ( (a+4)\(a^2-4a+16\) )
Step 1
Concept
Since \(64=4^3\), this is a sum of cubes. Exam tip: keep the signs (-) then (+) in the second bracket.
Step 2
Why this answer is correct
The correct answer is A. ( (a+4)\(a^2-4a+16\) ). Since \(64=4^3\), this is a sum of cubes. Exam tip: keep the signs (-) then (+) in the second bracket.
Step 3
Exam Tip
\(64=4^3\) इसलिए यह घनों के योग का रूप है। परीक्षा में दूसरे ब्रैकेट में चिन्ह (-) फिर (+) रखें।
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\(b^3-27\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(b^3-27\)?
#difference of cubes
#identity
#factorisation
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A ( (b-3)\(b^2+3b+9\) )
B ( (b+3)\(b^2-3b+9\) )
C ( (b-9)\(b^2+9b+81\) )
D ( (b-3)\(b^2-3b+9\) )
Explanation opens after your attempt
Correct Answer
A. ( (b-3)\(b^2+3b+9\) )
Step 1
Concept
Here \(27=3^3\) and it is a difference of cubes. Exam tip: in \(a^3-b^3\), the second bracket is \(a^2+ab+b^2\).
Step 2
Why this answer is correct
The correct answer is A. ( (b-3)\(b^2+3b+9\) ). Here \(27=3^3\) and it is a difference of cubes. Exam tip: in \(a^3-b^3\), the second bracket is \(a^2+ab+b^2\).
Step 3
Exam Tip
\(27=3^3\) है और यह घनों का अंतर है। परीक्षा में \(a^3-b^3\) में दूसरे ब्रैकेट के सभी पद धनात्मक जैसे \(a^2+ab+b^2\) होते हैं।
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\(x^2+6x+8\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+6x+8\).
#quadratic
#factorisation
#middle term
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A ( (x+2)(x+4) )
B ( (x-2)(x-4) )
C ( (x+1)(x+8) )
D ( (x+3)(x+3) )
Explanation opens after your attempt
Correct Answer
A. ( (x+2)(x+4) )
Step 1
Concept
The numbers (2) and (4) have sum (6) and product (8). Exam tip: check all options even in simple products.
Step 2
Why this answer is correct
The correct answer is A. ( (x+2)(x+4) ). The numbers (2) and (4) have sum (6) and product (8). Exam tip: check all options even in simple products.
Step 3
Exam Tip
(2) और (4) का योग (6) और गुणनफल (8) है। परीक्षा में छोटे गुणनफल वाले प्रश्न में भी सभी विकल्प जांचें।
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\(7x^2y-21xy^2+14xy\) का सर्वोत्तम गुणनखंड रूप क्या है?
What is the best factorised form of \(7x^2y-21xy^2+14xy\)?
#common factor
#polynomial
#factorisation
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A (7xy(x-3y+2))
B (7x\(xy-3y^2+2y\))
C (xy(7x-21y+14))
D (14xy(x-y+1))
Explanation opens after your attempt
Correct Answer
A. (7xy(x-3y+2))
Step 1
Concept
All three terms have (7xy) as the greatest common factor. Exam tip: the best factorised form takes out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (7xy(x-3y+2)). All three terms have (7xy) as the greatest common factor. Exam tip: the best factorised form takes out the greatest common factor.
Step 3
Exam Tip
तीनों पदों में (7xy) सबसे बड़ा सार्व गुणनखंड है। परीक्षा में सर्वोत्तम गुणनखंड रूप में सबसे बड़ा सामान्य गुणनखंड निकले।
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\(t^2-64\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(t^2-64\)?
#difference of squares
#factorisation
#identity
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A ( (t-8)(t+8) )
B ( (t-32)(t+2) )
C ( (t+8)2 )
D ( (t-8)2 )
Explanation opens after your attempt
Correct Answer
A. ( (t-8)(t+8) )
Step 1
Concept
Since \(64=8^2\), the difference of squares identity applies. Exam tip: recognising square numbers quickly saves time.
Step 2
Why this answer is correct
The correct answer is A. ( (t-8)(t+8) ). Since \(64=8^2\), the difference of squares identity applies. Exam tip: recognising square numbers quickly saves time.
Step 3
Exam Tip
\(64=8^2\) है इसलिए अंतर वर्ग पहचान लगेगी। परीक्षा में वर्ग संख्याओं को जल्दी पहचानना समय बचाता है।
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\(r^2+4rs+4s^2-9\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(r^2+4rs+4s^2-9\).
#mixed identity
#perfect square
#factorisation
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A ( (r+2s-3)(r+2s+3) )
B ( (r-2s-3)(r-2s+3) )
C ( (r+4s-9)(r+s+1) )
D ( (r+2s+3)2 )
Explanation opens after your attempt
Correct Answer
A. ( (r+2s-3)(r+2s+3) )
Step 1
Concept
First write \(r^2+4rs+4s^2\) as ((r+2s)2 ). Exam tip: apply difference of squares after forming a perfect square.
Step 2
Why this answer is correct
The correct answer is A. ( (r+2s-3)(r+2s+3) ). First write \(r^2+4rs+4s^2\) as ((r+2s)2 ). Exam tip: apply difference of squares after forming a perfect square.
Step 3
Exam Tip
पहले \(r^2+4rs+4s^2\) को ((r+2s)2 ) लिखें। परीक्षा में पूर्ण वर्ग के बाद अंतर वर्ग लगाएं।
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(xy-2x+4y-8) का गुणनखंड क्या है?
What is the factorisation of (xy-2x+4y-8)?
#grouping
#common binomial
#factorisation
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A ( (x+4)(y-2) )
B ( (x-4)(y+2) )
C ( (x+2)(y-4) )
D ( (x-8)(y+1) )
Explanation opens after your attempt
Correct Answer
A. ( (x+4)(y-2) )
Step 1
Concept
Grouping gives (x(y-2)+4(y-2)). Exam tip: pair suitable terms correctly while grouping.
Step 2
Why this answer is correct
The correct answer is A. ( (x+4)(y-2) ). Grouping gives (x(y-2)+4(y-2)). Exam tip: pair suitable terms correctly while grouping.
Step 3
Exam Tip
समूह बनाने पर (x(y-2)+4(y-2)) मिलता है। परीक्षा में पहले और तीसरे जैसे पदों को सही तरह जोड़ें।
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\(36a^2-b^2\) को गुणनखंडों में लिखिए।
Write \(36a^2-b^2\) in factors.
#difference of squares
#binomial
#factorisation
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A ( (6a-b)(6a+b) )
B ( (36a-b)(a+b) )
C ( (6a+b)2 )
D ( (6a-b)2 )
Explanation opens after your attempt
Correct Answer
A. ( (6a-b)(6a+b) )
Step 1
Concept
Since (36a-2 =(6a)2 ), this is a difference of two squares. Exam tip: treat variable squares like ordinary squares.
Step 2
Why this answer is correct
The correct answer is A. ( (6a-b)(6a+b) ). Since (36a-2 =(6a)2 ), this is a difference of two squares. Exam tip: treat variable squares like ordinary squares.
Step 3
Exam Tip
(36a-2 =(6a)2 ) है इसलिए यह दो वर्गों का अंतर है। परीक्षा में चर वाले वर्गों को भी सामान्य वर्गों की तरह पहचानें।
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\(k^2-15k+56\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(k^2-15k+56\)?
#quadratic
#factorisation
#signs
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A ( (k-7)(k-8) )
B ( (k+7)(k+8) )
C ( (k-4)(k-14) )
D ( (k-1)(k-56) )
Explanation opens after your attempt
Correct Answer
A. ( (k-7)(k-8) )
Step 1
Concept
The numbers (-7) and (-8) have sum (-15) and product (56). Exam tip: when the constant term is positive, signs are the same.
Step 2
Why this answer is correct
The correct answer is A. ( (k-7)(k-8) ). The numbers (-7) and (-8) have sum (-15) and product (56). Exam tip: when the constant term is positive, signs are the same.
Step 3
Exam Tip
(-7) और (-8) का योग (-15) और गुणनफल (56) है। परीक्षा में अंतिम पद धनात्मक होने पर चिन्ह समान होते हैं।
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\(x^2-y^2+2y-1\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-y^2+2y-1\).
#mixed identity
#difference of squares
#factorisation
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A ( (x-y+1)(x+y-1) )
B ( (x+y+1)(x-y-1) )
C ( (x-y-1)(x+y+1) )
D ( (x+y-1)2 )
Explanation opens after your attempt
Correct Answer
A. ( (x-y+1)(x+y-1) )
Step 1
Concept
Treat \(-y^2+2y-1\) as (-(y-1)2 ) to get (x-2 -(y-1)2 ). Exam tip: place the negative sign on the whole square.
Step 2
Why this answer is correct
The correct answer is A. ( (x-y+1)(x+y-1) ). Treat \(-y^2+2y-1\) as (-(y-1)2 ) to get (x-2 -(y-1)2 ). Exam tip: place the negative sign on the whole square.
Step 3
Exam Tip
\(-y^2+2y-1\) को (-(y-1)2 ) समझकर (x-2 -(y-1)2 ) बनता है। परीक्षा में ऋण चिन्ह को पूरे वर्ग पर लगाएं।
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\(2x^2+7x+3\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(2x^2+7x+3\)?
#quadratic
#ac method
#factorisation
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A ( (2x+1)(x+3) )
B ( (2x+3)(x+1) )
C ( (x+2)(2x+3) )
D ( (2x-1)(x-3) )
Explanation opens after your attempt
Correct Answer
A. ( (2x+1)(x+3) )
Step 1
Concept
Writing \(2x^2+6x+x+3\) and grouping gives the correct form. Exam tip: use the (ac) method to split the middle term.
Step 2
Why this answer is correct
The correct answer is A. ( (2x+1)(x+3) ). Writing \(2x^2+6x+x+3\) and grouping gives the correct form. Exam tip: use the (ac) method to split the middle term.
Step 3
Exam Tip
\(2x^2+6x+x+3\) लिखकर समूह बनाने से सही रूप मिलता है। परीक्षा में (ac) विधि से मध्य पद तोड़ें।
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\(3x^2+10x+8\) के गुणनखंड क्या हैं?
What are the factors of \(3x^2+10x+8\)?
#quadratic
#factorisation
#grouping
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A ( (3x+4)(x+2) )
B ( (3x+2)(x+4) )
C ( (x+4)(x+6) )
D ( (3x-4)(x-2) )
Explanation opens after your attempt
Correct Answer
A. ( (3x+4)(x+2) )
Step 1
Concept
Using \(3x^2+6x+4x+8\) gives common groups. Exam tip: you can also verify an option by expanding it.
Step 2
Why this answer is correct
The correct answer is A. ( (3x+4)(x+2) ). Using \(3x^2+6x+4x+8\) gives common groups. Exam tip: you can also verify an option by expanding it.
Step 3
Exam Tip
\(3x^2+6x+4x+8\) से समान समूह मिलते हैं। परीक्षा में फैलाकर विकल्प की जांच भी कर सकते हैं।
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\(12a^2-27b^2\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(12a^2-27b^2\)?
#common factor
#difference of squares
#factorisation
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A (3(2a-3b)(2a+3b))
B ( (12a-27b)(a+b) )
C (3\(4a^2-9b^2\))
D ( (6a-9b)(2a+3b) )
Explanation opens after your attempt
Correct Answer
A. (3(2a-3b)(2a+3b))
Step 1
Concept
Taking out (3) first gives \(4a^2-9b^2\). Exam tip: use both common factor and identity.
Step 2
Why this answer is correct
The correct answer is A. (3(2a-3b)(2a+3b)). Taking out (3) first gives \(4a^2-9b^2\). Exam tip: use both common factor and identity.
Step 3
Exam Tip
पहले (3) निकालने पर \(4a^2-9b^2\) मिलता है। परीक्षा में सार्व गुणनखंड और पहचान दोनों का उपयोग करें।
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\(a^2+b^2+2ab-c^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(a^2+b^2+2ab-c^2\).
#mixed identity
#perfect square
#difference of squares
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A ( (a+b-c)(a+b+c) )
B ( (a-b-c)(a-b+c) )
C ( (a+b)2 +c-2 )
D ( (a+c-b)(a+c+b) )
Explanation opens after your attempt
Correct Answer
A. ( (a+b-c)(a+b+c) )
Step 1
Concept
First convert \(a^2+b^2+2ab\) into ((a+b)2 ). Exam tip: turn three terms into a perfect square before proceeding.
Step 2
Why this answer is correct
The correct answer is A. ( (a+b-c)(a+b+c) ). First convert \(a^2+b^2+2ab\) into ((a+b)2 ). Exam tip: turn three terms into a perfect square before proceeding.
Step 3
Exam Tip
पहले \(a^2+b^2+2ab\) को ((a+b)2 ) बनाएं। परीक्षा में तीन पदों को पूर्ण वर्ग में बदलकर आगे बढ़ें।
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\(4x^2-20x+25\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(4x^2-20x+25\)?
#perfect square trinomial
#factorisation
#identity
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A ( (2x-5)2 )
B ( (2x+5)2 )
C ( (4x-5)2 )
D ( (2x-25)(2x-1) )
Explanation opens after your attempt
Correct Answer
A. ( (2x-5)2 )
Step 1
Concept
It is ((2x)2 -2\cdot2x\cdot5+52 ). Exam tip: confirm the middle term equals (2ab).
Step 2
Why this answer is correct
The correct answer is A. ( (2x-5)2 ). It is ((2x)2 -2\cdot2x\cdot5+52 ). Exam tip: confirm the middle term equals (2ab).
Step 3
Exam Tip
यह ((2x)2 -2\cdot2x\cdot5+52 ) है। परीक्षा में (2ab) के बराबर मध्य पद की पुष्टि करें।
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(6pq+9p+4q+6) का गुणनखंड क्या है?
What is the factorisation of (6pq+9p+4q+6)?
#grouping
#common binomial
#factorisation
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A ( (3p+2)(2q+3) )
B ( (6p+4)(q+3) )
C ( (3p+4)(2q+6) )
D ( (2p+3)(3q+2) )
Explanation opens after your attempt
Correct Answer
A. ( (3p+2)(2q+3) )
Step 1
Concept
Grouping gives (3p(2q+3)+2(2q+3)). Exam tip: take out the common binomial once it appears.
Step 2
Why this answer is correct
The correct answer is A. ( (3p+2)(2q+3) ). Grouping gives (3p(2q+3)+2(2q+3)). Exam tip: take out the common binomial once it appears.
Step 3
Exam Tip
समूह बनाने पर (3p(2q+3)+2(2q+3)) मिलता है। परीक्षा में समान द्विपद मिलने पर उसे बाहर निकालें।
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\(64m^3+125n^3\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(64m^3+125n^3\).
#sum of cubes
#factorisation
#identity
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A ( (4m+5n)\(16m^2-20mn+25n^2\) )
B ( (4m-5n)\(16m^2+20mn+25n^2\) )
C ( (4m+5n)\(16m^2+20mn+25n^2\) )
D ( (64m+125n)\(m^2-mn+n^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (4m+5n)\(16m^2-20mn+25n^2\) )
Step 1
Concept
It is ((4m)3 +(5n)3 ). Exam tip: in the sum of cubes, the middle term of the second bracket is negative.
Step 2
Why this answer is correct
The correct answer is A. ( (4m+5n)\(16m^2-20mn+25n^2\) ). It is ((4m)3 +(5n)3 ). Exam tip: in the sum of cubes, the middle term of the second bracket is negative.
Step 3
Exam Tip
यह ((4m)3 +(5n)3 ) है। परीक्षा में घनों के योग में दूसरे ब्रैकेट का मध्य पद ऋणात्मक होता है।
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\(125x^3-216y^3\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(125x^3-216y^3\)?
#difference of cubes
#factorisation
#identity
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A ( (5x-6y)\(25x^2+30xy+36y^2\) )
B ( (5x+6y)\(25x^2-30xy+36y^2\) )
C ( (5x-6y)\(25x^2-30xy+36y^2\) )
D ( (125x-216y)\(x^2+xy+y^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (5x-6y)\(25x^2+30xy+36y^2\) )
Step 1
Concept
Here (125x-3 =(5x)3 ) and (216y-3 =(6y)3 ). Exam tip: in difference of cubes, signs in the second bracket are (+) and (+).
Step 2
Why this answer is correct
The correct answer is A. ( (5x-6y)\(25x^2+30xy+36y^2\) ). Here (125x-3 =(5x)3 ) and (216y-3 =(6y)3 ). Exam tip: in difference of cubes, signs in the second bracket are (+) and (+).
Step 3
Exam Tip
(125x-3 =(5x)3 ) और (216y-3 =(6y)3 ) हैं। परीक्षा में घनों के अंतर में दूसरे ब्रैकेट के चिन्ह (+) और (+) होते हैं।
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\(2a^2-11a+15\) का गुणनखंड रूप क्या है?
What is the factorised form of \(2a^2-11a+15\)?
#quadratic
#ac method
#factorisation
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A ( (2a-5)(a-3) )
B ( (2a-3)(a-5) )
C ( (a-5)(a-6) )
D ( (2a+5)(a+3) )
Explanation opens after your attempt
Correct Answer
A. ( (2a-5)(a-3) )
Step 1
Concept
Using \(2a^2-6a-5a+15\) and grouping gives the answer. Exam tip: choose the pair with product (30) and sum (-11).
Step 2
Why this answer is correct
The correct answer is A. ( (2a-5)(a-3) ). Using \(2a^2-6a-5a+15\) and grouping gives the answer. Exam tip: choose the pair with product (30) and sum (-11).
Step 3
Exam Tip
\(2a^2-6a-5a+15\) से समूह बनाकर उत्तर मिलता है। परीक्षा में (ac=30) और योग (-11) वाली जोड़ी चुनें।
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\(3y^2-14y-5\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(3y^2-14y-5\)?
#quadratic
#factorisation
#verification
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A ( (3y+1)(y-5) )
B ( (3y-1)(y+5) )
C ( (y-15)(3y+1) )
D ( (3y-5)(y+1) )
Explanation opens after your attempt
Correct Answer
A. ( (3y+1)(y-5) )
Step 1
Concept
Expanding gives \(3y^2-15y+y-5\), which is \(3y^2-14y-5\). Exam tip: verify quickly by expanding the option.
Step 2
Why this answer is correct
The correct answer is A. ( (3y+1)(y-5) ). Expanding gives \(3y^2-15y+y-5\), which is \(3y^2-14y-5\). Exam tip: verify quickly by expanding the option.
Step 3
Exam Tip
फैलाने पर \(3y^2-15y+y-5\) मिलता है जो \(3y^2-14y-5\) है। परीक्षा में विकल्प को फैलाकर जल्दी जांचें।
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\(9x^2-1+6xy+y^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(9x^2-1+6xy+y^2\).
#mixed identity
#perfect square
#difference of squares
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A ( (3x+y-1)(3x+y+1) )
B ( (3x-y-1)(3x-y+1) )
C ( (9x+y-1)(x+y+1) )
D ( (3x+y+1)2 )
Explanation opens after your attempt
Correct Answer
A. ( (3x+y-1)(3x+y+1) )
Step 1
Concept
Write \(9x^2+6xy+y^2\) as ((3x+y)2 ) and use difference of squares with (-1). Exam tip: arranging terms properly helps.
Step 2
Why this answer is correct
The correct answer is A. ( (3x+y-1)(3x+y+1) ). Write \(9x^2+6xy+y^2\) as ((3x+y)2 ) and use difference of squares with (-1). Exam tip: arranging terms properly helps.
Step 3
Exam Tip
\(9x^2+6xy+y^2\) को ((3x+y)2 ) बनाकर (-1) के साथ अंतर वर्ग लगाएं। परीक्षा में पदों को उचित क्रम में लगाना सहायक है।
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\(15x^2-20xy\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(15x^2-20xy\)?
#common factor
#factorisation
#monomial
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A (5x(3x-4y))
B (5\(3x^2-4xy\))
C (x(15x-20y))
D (10x(2x-2y))
Explanation opens after your attempt
Correct Answer
A. (5x(3x-4y))
Step 1
Concept
Both terms have (5x) as the greatest common factor. Exam tip: take the common factor from both numerical and algebraic parts.
Step 2
Why this answer is correct
The correct answer is A. (5x(3x-4y)). Both terms have (5x) as the greatest common factor. Exam tip: take the common factor from both numerical and algebraic parts.
Step 3
Exam Tip
दोनों पदों में (5x) सबसे बड़ा सार्व गुणनखंड है। परीक्षा में संख्यात्मक और बीजीय दोनों भागों का सार्व गुणनखंड लें।
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\(x^2+5x-24\) के गुणनखंड क्या हैं?
What are the factors of \(x^2+5x-24\)?
#quadratic
#factorisation
#sign choice
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A ( (x+8)(x-3) )
B ( (x-8)(x+3) )
C ( (x+6)(x-4) )
D ( (x+12)(x-2) )
Explanation opens after your attempt
Correct Answer
A. ( (x+8)(x-3) )
Step 1
Concept
The numbers (8) and (-3) have sum (5) and product (-24). Exam tip: with opposite signs, the larger magnitude gives the sign of the middle term.
Step 2
Why this answer is correct
The correct answer is A. ( (x+8)(x-3) ). The numbers (8) and (-3) have sum (5) and product (-24). Exam tip: with opposite signs, the larger magnitude gives the sign of the middle term.
Step 3
Exam Tip
(8) और (-3) का योग (5) और गुणनफल (-24) है। परीक्षा में अलग चिन्ह वाले गुणनखंडों में बड़ा परिमाण मध्य पद का चिन्ह देता है।
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\(a^2-b^2-a+b\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(a^2-b^2-a+b\)?
#difference of squares
#grouping
#factorisation
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A ( (a-b)(a+b-1) )
B ( (a+b)(a-b-1) )
C ( (a-b)(a+b+1) )
D ( (a+b-1)2 )
Explanation opens after your attempt
Correct Answer
A. ( (a-b)(a+b-1) )
Step 1
Concept
Write \(a^2-b^2\) as ((a-b)(a+b)) and (-a+b) as (-(a-b)). Exam tip: take common ((a-b)) out.
Step 2
Why this answer is correct
The correct answer is A. ( (a-b)(a+b-1) ). Write \(a^2-b^2\) as ((a-b)(a+b)) and (-a+b) as (-(a-b)). Exam tip: take common ((a-b)) out.
Step 3
Exam Tip
\(a^2-b^2\) को ((a-b)(a+b)) और (-a+b) को (-(a-b)) लिखें। परीक्षा में समान ((a-b)) को बाहर निकालें।
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\(4x^2+4x-15\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(4x^2+4x-15\)?
#quadratic
#factorisation
#verification
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A ( (2x-5)(2x+3) )
B ( (2x+5)(2x-3) )
C ( (4x+5)(x-3) )
D ( (2x+15)(2x-1) )
Explanation opens after your attempt
Correct Answer
B. ( (2x+5)(2x-3) )
Step 1
Concept
Expanding gives ( (2x+5)(2x-3)=4x-2 +4x-15 ). Exam tip: expand the option and check both the middle term and constant term.
Step 2
Why this answer is correct
The correct answer is B. ( (2x+5)(2x-3) ). Expanding gives ( (2x+5)(2x-3)=4x-2 +4x-15 ). Exam tip: expand the option and check both the middle term and constant term.
Step 3
Exam Tip
फैलाने पर ( (2x+5)(2x-3)=4x-2 +4x-15 ) मिलता है। परीक्षा में विकल्प को फैलाकर मध्य पद और अंतिम पद दोनों जांचें।
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\(6a^2b+9ab^2\) का सही गुणनखंड रूप कौन-सा है?
Which is the correct factorised form of \(6a^2b+9ab^2\)?
#factorisation
#common factor
#monomials
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A (3ab(2a+3b)) / सही रूप
B (3a\(2ab+3b^2\)) / पूरा सरल नहीं
C (ab(6a+9b)) / पूरा समान गुणनखंड नहीं निकला
D (3ab(2a-3b)) / गलत चिन्ह
Explanation opens after your attempt
Correct Answer
A. (3ab(2a+3b)) / सही रूप
Step 1
Concept
The common factor is (3ab), leaving (2a+3b). In exams check both numerical and algebraic common factors.
Step 2
Why this answer is correct
The correct answer is A. (3ab(2a+3b)) / सही रूप. The common factor is (3ab), leaving (2a+3b). In exams check both numerical and algebraic common factors.
Step 3
Exam Tip
समान गुणनखंड (3ab) है और शेष (2a+3b) बचता है। परीक्षा में संख्यात्मक और बीजीय दोनों समान गुणनखंड देखें।
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\(x^2-49\) को गुणनखंडित करें।
Factorise \(x^2-49\).
#factorisation
#difference of squares
#identity
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A ((x-7)(x+7)) / वर्गों का अंतर
B ((x-49)(x+49)) / गलत वर्गमूल
C ((x-7)2 ) / अंतर का वर्ग
D (x(x-49)) / गलत समान गुणनखंड
Explanation opens after your attempt
Correct Answer
A. ((x-7)(x+7)) / वर्गों का अंतर
Step 1
Concept
Since \(49=7^2\), (x-2 -49=(x-7)(x+7)). In exams take square roots in difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((x-7)(x+7)) / वर्गों का अंतर. Since \(49=7^2\), (x-2 -49=(x-7)(x+7)). In exams take square roots in difference of squares.
Step 3
Exam Tip
\(49=7^2\), इसलिए (x-2 -49=(x-7)(x+7)) है। परीक्षा में वर्गों के अंतर में वर्गमूल लें।
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\(y^2+12y+36\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(y^2+12y+36\)?
#factorisation
#perfect square
#trinomial
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A ((y+6)2 ) / पूर्ण वर्ग
B ((y-6)2 ) / गलत चिन्ह
C ((y+3)(y+12)) / मध्य पद गलत
D ((y+4)(y+9)) / गुणनफल सही नहीं
Explanation opens after your attempt
Correct Answer
A. ((y+6)2 ) / पूर्ण वर्ग
Step 1
Concept
\(36=6^2\) and \(12y=2\cdot y\cdot6\). In exams identify perfect square trinomials.
Step 2
Why this answer is correct
The correct answer is A. ((y+6)2 ) / पूर्ण वर्ग. \(36=6^2\) and \(12y=2\cdot y\cdot6\). In exams identify perfect square trinomials.
Step 3
Exam Tip
\(36=6^2\) और \(12y=2\cdot y\cdot6\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।
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\(m^2-10m+25\) को किस रूप में लिखा जाएगा?
How will \(m^2-10m+25\) be written in factorised form?
#factorisation
#perfect square
#negative middle
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A ((m+5)2 ) / गलत चिन्ह
B ((m-5 )2 ) / सही पूर्ण वर्ग
C ((m-10 )(m+25)) / गलत गुणनखंड
D ((m-25 )2 ) / गलत स्थिर भाग
Explanation opens after your attempt
Correct Answer
B. ((m-5 )2 ) / सही पूर्ण वर्ग
Step 1
Concept
\(25=5^2\) and the middle term is \(-2\cdot m\cdot5\). In exams always check the sign of the middle term.
Step 2
Why this answer is correct
The correct answer is B. ((m-5 )2 ) / सही पूर्ण वर्ग. \(25=5^2\) and the middle term is \(-2\cdot m\cdot5\). In exams always check the sign of the middle term.
Step 3
Exam Tip
\(25=5^2\) और मध्य पद \(-2\cdot m\cdot5\) है। परीक्षा में मध्य पद का चिन्ह जरूर देखें।
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\(p^2-p-20\) का सही गुणनखंड रूप चुनें।
Choose the correct factorised form of \(p^2-p-20\).
#factorisation
#signed factors
#trinomial
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A ((p+4)(p-5)) / सही रूप
B ((p-4)(p+5)) / मध्य पद गलत
C ((p-2)(p+10)) / मध्य पद गलत
D ((p+20)(p-1)) / गुणनफल तो सही पर मध्य गलत
Explanation opens after your attempt
Correct Answer
A. ((p+4)(p-5)) / सही रूप
Step 1
Concept
Here (4+(-5)=-1) and (4\cdot(-5)=-20). In exams use opposite signs for a negative constant term.
Step 2
Why this answer is correct
The correct answer is A. ((p+4)(p-5)) / सही रूप. Here (4+(-5)=-1) and (4\cdot(-5)=-20). In exams use opposite signs for a negative constant term.
Step 3
Exam Tip
(4+(-5)=-1) और (4\cdot(-5)=-20) है। परीक्षा में ऋणात्मक स्थिर पद के लिए विपरीत चिन्ह लें।
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समूहीकरण विधि से (ax+ay+bx+by) का गुणनखंड रूप क्या है?
Using grouping, what is the factorised form of (ax+ay+bx+by)?
#factorisation
#grouping
#common binomial
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A (a(x+y)+b(x+y)) / आंशिक रूप
B ((a+b)(x+y)) / पूर्ण गुणनखंड
C ((a+y)(b+x)) / गलत समूह
D (ab(x+y)) / गलत समान गुणनखंड
Explanation opens after your attempt
Correct Answer
B. ((a+b)(x+y)) / पूर्ण गुणनखंड
Step 1
Concept
First it becomes (a(x+y)+b(x+y)), then ((x+y)) is taken common. In exams look for a common binomial.
Step 2
Why this answer is correct
The correct answer is B. ((a+b)(x+y)) / पूर्ण गुणनखंड. First it becomes (a(x+y)+b(x+y)), then ((x+y)) is taken common. In exams look for a common binomial.
Step 3
Exam Tip
पहले (a(x+y)+b(x+y)) बनता है और फिर ((x+y)) समान गुणनखंड निकलता है। परीक्षा में समान द्विपद खोजें।
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\(2x^2+7x+3\) के गुणनखंड कौन-से हैं?
What are the factors of \(2x^2+7x+3\)?
#factorisation
#quadratic
#split middle
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A ((2x+1)(x+3)) / सही गुणनखंड
B ((2x+3)(x+1)) / मध्य पद गलत
C ((x+1)(x+3)) / अग्र गुणांक गलत
D ((2x-1)(x-3)) / चिन्ह गलत
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x+3)) / सही गुणनखंड
Step 1
Concept
((2x+1)(x+3)=2x-2 +7x+3). In exams verify quickly by multiplication.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x+3)) / सही गुणनखंड. ((2x+1)(x+3)=2x-2 +7x+3). In exams verify quickly by multiplication.
Step 3
Exam Tip
((2x+1)(x+3)=2x-2 +7x+3) होता है। परीक्षा में गुणा करके तुरंत जांचें।
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\(4x^2-9\) को गुणनखंडित करें।
Factorise \(4x^2-9\).
#factorisation
#difference of squares
#identity
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A ((2x-3)(2x+3)) / सही वर्गों का अंतर
B ((4x-9)(4x+9)) / गलत वर्गमूल
C ((2x-3)2 ) / पूर्ण वर्ग नहीं
D ((x-3)(4x+3)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((2x-3)(2x+3)) / सही वर्गों का अंतर
Step 1
Concept
(4x-2 =(2x)2 ) and \(9=3^2\), so it factors as a difference of squares. In exams identify both squares.
Step 2
Why this answer is correct
The correct answer is A. ((2x-3)(2x+3)) / सही वर्गों का अंतर. (4x-2 =(2x)2 ) and \(9=3^2\), so it factors as a difference of squares. In exams identify both squares.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(9=3^2\), इसलिए अंतर का गुणनखंड बनता है। परीक्षा में दोनों वर्ग पहचानें।
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\(3x^2+12x\) का सबसे सरल गुणनखंड रूप क्या है?
What is the simplest factorised form of \(3x^2+12x\)?
#common factor
#gcf
#factorisation
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A (3x(x+4)) / सही समान गुणनखंड
B (3\(x^2+4x\)) / पूरा सरल नहीं
C (x(3x+12)) / पूरा समान गुणनखंड नहीं निकला
D (12x(x+3)) / गलत गुणनखंड
Explanation opens after your attempt
Correct Answer
A. (3x(x+4)) / सही समान गुणनखंड
Step 1
Concept
The greatest common factor in both terms is (3x). In exams it is better to take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (3x(x+4)) / सही समान गुणनखंड. The greatest common factor in both terms is (3x). In exams it is better to take out the greatest common factor.
Step 3
Exam Tip
दोनों पदों में सबसे बड़ा समान गुणनखंड (3x) है। परीक्षा में सबसे बड़ा समान गुणनखंड निकालना बेहतर है।
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\(a^2+2ab+b^2\) का गुणनखंड रूप कौन-सा है?
Which is the factorised form of \(a^2+2ab+b^2\)?
#identity
#perfect square
#factorisation
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A ((a+b)2 ) / सही पूर्ण वर्ग
B ((a-b)2 ) / गलत चिन्ह
C ((a+b)(a-b)) / वर्गों का अंतर
D ((a+2b)(a+b)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((a+b)2 ) / सही पूर्ण वर्ग
Step 1
Concept
This is the square of a sum identity. In exams identify ((a+b)2 ) by the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is A. ((a+b)2 ) / सही पूर्ण वर्ग. This is the square of a sum identity. In exams identify ((a+b)2 ) by the middle term (2ab).
Step 3
Exam Tip
यह योग के वर्ग की पहचान है। परीक्षा में (2ab) मध्य पद देखकर ((a+b)2 ) पहचानें।
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\(r^2-2rs+s^2\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(r^2-2rs+s^2\)?
#identity
#perfect square
#factorisation
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A ((r+s)2 ) / गलत चिन्ह
B ((r-s)2 ) / सही पूर्ण वर्ग
C ((r-s)(r+s)) / वर्गों का अंतर
D ((r-2s)(r+s)) / गलत मध्य पद
Explanation opens after your attempt
Correct Answer
B. ((r-s)2 ) / सही पूर्ण वर्ग
Step 1
Concept
This is the square of a difference identity. In exams choose the subtraction perfect square when you see (-2rs).
Step 2
Why this answer is correct
The correct answer is B. ((r-s)2 ) / सही पूर्ण वर्ग. This is the square of a difference identity. In exams choose the subtraction perfect square when you see (-2rs).
Step 3
Exam Tip
यह अंतर के वर्ग की पहचान है। परीक्षा में (-2rs) देखकर घटाव वाला पूर्ण वर्ग चुनें।
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\(16a^2-b^2\) का सही गुणनखंड रूप चुनें।
Choose the correct factorised form of \(16a^2-b^2\).
#difference of squares
#factorisation
#algebraic identity
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A ((4a-b)(4a+b)) / सही उत्तर
B ((16a-b)(16a+b)) / गलत वर्गमूल
C ((4a-b)2 ) / अंतर का वर्ग
D ((8a-b)(2a+b)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((4a-b)(4a+b)) / सही उत्तर
Step 1
Concept
(16a-2 =(4a)2 ), so the difference of squares applies. In exams take the square roots correctly.
Step 2
Why this answer is correct
The correct answer is A. ((4a-b)(4a+b)) / सही उत्तर. (16a-2 =(4a)2 ), so the difference of squares applies. In exams take the square roots correctly.
Step 3
Exam Tip
(16a-2 =(4a)2 ) है, इसलिए वर्गों का अंतर लागू होता है। परीक्षा में वर्गमूल को सही लें।
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\(x^2+11x+30\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+11x+30\)?
#trinomial
#factorisation
#split middle
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A ((x+5)(x+6)) / सही रूप
B ((x+3)(x+10)) / मध्य पद गलत
C ((x-5)(x-6)) / चिन्ह गलत
D ((x+1)(x+30)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x+6)) / सही रूप
Step 1
Concept
Here (5+6=11) and \(5\cdot6=30\). In exams check the sum of factors of the constant term.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x+6)) / सही रूप. Here (5+6=11) and \(5\cdot6=30\). In exams check the sum of factors of the constant term.
Step 3
Exam Tip
(5+6=11) और \(5\cdot6=30\) है। परीक्षा में स्थिर पद के गुणनखंडों का योग देखें।
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\(x^2-13x+42\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2-13x+42\)?
#trinomial
#negative factors
#factorisation
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A ((x-6)(x-7)) / सही गुणनखंड
B ((x+6)(x+7)) / मध्य पद धनात्मक
C ((x-3)(x-14)) / मध्य पद गलत
D ((x-1)(x-42)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x-6)(x-7)) / सही गुणनखंड
Step 1
Concept
(-6+(-7)=-13) and ((-6)(-7)=42). In exams use two negative signs when the constant is positive and the middle term is negative.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)(x-7)) / सही गुणनखंड. (-6+(-7)=-13) and ((-6)(-7)=42). In exams use two negative signs when the constant is positive and the middle term is negative.
Step 3
Exam Tip
(-6+(-7)=-13) और ((-6)(-7)=42) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद के लिए दोनों चिन्ह ऋणात्मक लें।
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(5xy-10x+3y-6) को समूहीकरण से गुणनखंडित करें।
Factorise (5xy-10x+3y-6) by grouping.
#grouping
#common binomial
#factorisation
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A ((5x+3)(y-2)) / सही रूप
B ((5x-3)(y+2)) / चिन्ह गलत
C ((x+3)(5y-2)) / गलत समूह
D ((5x+3)(y+2)) / स्थिर पद गलत
Explanation opens after your attempt
Correct Answer
A. ((5x+3)(y-2)) / सही रूप
Step 1
Concept
The grouping gives (5x(y-2)+3(y-2)). In exams take the common bracket as the next common factor.
Step 2
Why this answer is correct
The correct answer is A. ((5x+3)(y-2)) / सही रूप. The grouping gives (5x(y-2)+3(y-2)). In exams take the common bracket as the next common factor.
Step 3
Exam Tip
समूह (5x(y-2)+3(y-2)) बनता है। परीक्षा में समान कोष्ठक को फिर समान गुणनखंड लें।
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\(2a^2-8b^2\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(2a^2-8b^2\)?
#common factor
#difference of squares
#factorisation
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A (2(a-2b)(a+2b)) / सही रूप
B (2(a-b)(a+b)) / \(8b^2\) नहीं बनेगा
C ((2a-8b)(a+b)) / गलत रूप
D (2(a-4b)2 ) / गलत पहचान
Explanation opens after your attempt
Correct Answer
A. (2(a-2b)(a+2b)) / सही रूप
Step 1
Concept
First take common (2), then \(a^2-4b^2\) is a difference of squares. In exams apply the identity after taking the common factor.
Step 2
Why this answer is correct
The correct answer is A. (2(a-2b)(a+2b)) / सही रूप. First take common (2), then \(a^2-4b^2\) is a difference of squares. In exams apply the identity after taking the common factor.
Step 3
Exam Tip
पहले (2) समान गुणनखंड निकालें, फिर \(a^2-4b^2\) वर्गों का अंतर है। परीक्षा में समान गुणनखंड के बाद पहचान लगाएं।
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\(9x^2+24xy+16y^2\) का गुणनखंड रूप कौन-सा है?
Which is the factorised form of \(9x^2+24xy+16y^2\)?
#perfect square
#identity
#factorisation
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A ((3x+4y)2 ) / सही पूर्ण वर्ग
B ((3x-4y)2 ) / चिन्ह गलत
C ((9x+16y)2 ) / गलत वर्गमूल
D ((3x+8y)(3x+2y)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((3x+4y)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(9x-2 =(3x)2 ), (16y-2 =(4y)2 ), and the middle is (24xy). In exams identify the two square terms first.
Step 2
Why this answer is correct
The correct answer is A. ((3x+4y)2 ) / सही पूर्ण वर्ग. (9x-2 =(3x)2 ), (16y-2 =(4y)2 ), and the middle is (24xy). In exams identify the two square terms first.
Step 3
Exam Tip
(9x-2 =(3x)2 ), (16y-2 =(4y)2 ) और मध्य (24xy) है। परीक्षा में पहले दोनों वर्ग पद पहचानें।
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\(25p^2-30pq+9q^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(25p^2-30pq+9q^2\)?
#perfect square
#negative middle
#factorisation
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A ((5p-3q)2 ) / सही पूर्ण वर्ग
B ((5p+3q)2 ) / गलत चिन्ह
C ((25p-9q)2 ) / गलत जड़
D ((5p-9q)(5p-q)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((5p-3q)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(25p-2 =(5p)2 ), (9q-2 =(3q)2 ), and the middle term is negative. In exams choose the correct square by the sign.
Step 2
Why this answer is correct
The correct answer is A. ((5p-3q)2 ) / सही पूर्ण वर्ग. (25p-2 =(5p)2 ), (9q-2 =(3q)2 ), and the middle term is negative. In exams choose the correct square by the sign.
Step 3
Exam Tip
(25p-2 =(5p)2 ), (9q-2 =(3q)2 ) और मध्य पद ऋणात्मक है। परीक्षा में चिन्ह से सही वर्ग चुनें।
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\(x^2-64y^2\) को गुणनखंडित करें।
Factorise \(x^2-64y^2\).
#difference of squares
#variables
#factorisation
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A ((x-8y)(x+8y)) / सही वर्गों का अंतर
B ((x-64y)(x+64y)) / गलत वर्गमूल
C ((x-8y)2 ) / पूर्ण वर्ग नहीं
D ((x-4y)(x+16y)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((x-8y)(x+8y)) / सही वर्गों का अंतर
Step 1
Concept
(64y-2 =(8y)2 ), so apply difference of squares. In exams take square roots with variables.
Step 2
Why this answer is correct
The correct answer is A. ((x-8y)(x+8y)) / सही वर्गों का अंतर. (64y-2 =(8y)2 ), so apply difference of squares. In exams take square roots with variables.
Step 3
Exam Tip
(64y-2 =(8y)2 ), इसलिए वर्गों का अंतर लगाएं। परीक्षा में चर सहित वर्गमूल लें।
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\(x^2+2x-15\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2+2x-15\)?
#signed trinomial
#factorisation
#split middle
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A ((x+5)(x-3)) / सही गुणनखंड
B ((x-5)(x+3)) / मध्य पद गलत
C ((x+1)(x-15)) / मध्य पद गलत
D ((x+3)(x+5)) / स्थिर पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x-3)) / सही गुणनखंड
Step 1
Concept
Here (5+(-3)=2) and (5\cdot(-3)=-15). In exams check opposite signs when the constant is negative.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x-3)) / सही गुणनखंड. Here (5+(-3)=2) and (5\cdot(-3)=-15). In exams check opposite signs when the constant is negative.
Step 3
Exam Tip
(5+(-3)=2) और (5\cdot(-3)=-15) है। परीक्षा में ऋणात्मक स्थिर पद पर विपरीत चिन्ह जांचें।
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\(2x^2-5x-3\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(2x^2-5x-3\)?
#quadratic
#factorisation
#signed factors
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A ((2x+1)(x-3)) / सही रूप
B ((2x-1)(x+3)) / मध्य पद गलत
C ((x-1)(2x+3)) / मध्य पद गलत
D ((2x-3)(x+1)) / स्थिर पद गलत
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x-3)) / सही रूप
Step 1
Concept
((2x+1)(x-3)=2x-2 -5x-3). In exams expanding options is useful for checking.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x-3)) / सही रूप. ((2x+1)(x-3)=2x-2 -5x-3). In exams expanding options is useful for checking.
Step 3
Exam Tip
((2x+1)(x-3)=2x-2 -5x-3) है। परीक्षा में विकल्पों को फैलाकर जांचना उपयोगी है।
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\(4m^2+4mn+n^2\) का गुणनखंड रूप चुनें।
Choose the factorised form of \(4m^2+4mn+n^2\).
#perfect square
#factorisation
#identity
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A ((2m+n)2 ) / सही पूर्ण वर्ग
B ((2m-n)2 ) / चिन्ह गलत
C ((4m+n)2 ) / गलत वर्गमूल
D ((m+n)(4m+n)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((2m+n)2 ) / सही पूर्ण वर्ग
Step 1
Concept
It is the square of the sum of (2m) and (n). In exams check \(4mn=2\cdot2m\cdot n\).
Step 2
Why this answer is correct
The correct answer is A. ((2m+n)2 ) / सही पूर्ण वर्ग. It is the square of the sum of (2m) and (n). In exams check \(4mn=2\cdot2m\cdot n\).
Step 3
Exam Tip
यह (2m) और (n) के योग का वर्ग है। परीक्षा में \(4mn=2\cdot2m\cdot n\) जांचें।
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\(7x^2+14xy\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(7x^2+14xy\)?
#common factor
#monomial
#factorisation
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A (7x(x+2y)) / सही समान गुणनखंड
B (7\(x^2+2xy\)) / पूरा सरल नहीं
C (x(7x+14y)) / पूरा समान गुणनखंड नहीं
D (14x(x+y)) / गलत गुणनखंड
Explanation opens after your attempt
Correct Answer
A. (7x(x+2y)) / सही समान गुणनखंड
Step 1
Concept
The common factor is (7x). In exams include variables as well as numbers in the common factor.
Step 2
Why this answer is correct
The correct answer is A. (7x(x+2y)) / सही समान गुणनखंड. The common factor is (7x). In exams include variables as well as numbers in the common factor.
Step 3
Exam Tip
समान गुणनखंड (7x) है। परीक्षा में केवल संख्या नहीं, चर भी समान गुणनखंड में लें।
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(ab-ac+db-dc) को समूहीकरण से गुणनखंडित करें।
Factorise (ab-ac+db-dc) by grouping.
#grouping
#common binomial
#factorisation
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A ((a+d)(b-c)) / सही रूप
B ((a-d)(b+c)) / चिन्ह गलत
C ((a+c)(b-d)) / गलत समूह
D ((ab+dc)(a-c)) / गलत रूप
Explanation opens after your attempt
Correct Answer
A. ((a+d)(b-c)) / सही रूप
Step 1
Concept
The grouping gives (a(b-c)+d(b-c)). In exams make the same binomial in both groups.
Step 2
Why this answer is correct
The correct answer is A. ((a+d)(b-c)) / सही रूप. The grouping gives (a(b-c)+d(b-c)). In exams make the same binomial in both groups.
Step 3
Exam Tip
समूह (a(b-c)+d(b-c)) बनता है। परीक्षा में दोनों समूहों में समान द्विपद बनाएं।
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\(81-z^2\) का गुणनखंड रूप कौन-सा है?
Which is the factorised form of \(81-z^2\)?
#difference of squares
#factorisation
#identity
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A ((9-z)(9+z)) / सही उत्तर
B ((81-z)(81+z)) / गलत वर्गमूल
C ((z-9)(z+9)) / चिन्ह से मूल अभिव्यक्ति उलटती है
D ((9-z)2 ) / पूर्ण वर्ग नहीं
Explanation opens after your attempt
Correct Answer
A. ((9-z)(9+z)) / सही उत्तर
Step 1
Concept
\(81=9^2\), so it is \(9^2-z^2\). In exams identify the larger and smaller squares first.
Step 2
Why this answer is correct
The correct answer is A. ((9-z)(9+z)) / सही उत्तर. \(81=9^2\), so it is \(9^2-z^2\). In exams identify the larger and smaller squares first.
Step 3
Exam Tip
\(81=9^2\), इसलिए यह \(9^2-z^2\) है। परीक्षा में पहले बड़ा वर्ग और छोटा वर्ग पहचानें।
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\(x^2-3x-18\) के गुणनखंड क्या हैं?
What are the factors of \(x^2-3x-18\)?
#trinomial
#signed factors
#factorisation
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A ((x-6)(x+3)) / सही गुणनखंड
B ((x+6)(x-3)) / मध्य पद गलत
C ((x-9)(x+2)) / मध्य पद गलत
D ((x-18)(x+1)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x-6)(x+3)) / सही गुणनखंड
Step 1
Concept
(-6+3=-3) and ((-6)(3)=-18). In exams choose the sign of the larger magnitude according to the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)(x+3)) / सही गुणनखंड. (-6+3=-3) and ((-6)(3)=-18). In exams choose the sign of the larger magnitude according to the middle term.
Step 3
Exam Tip
(-6+3=-3) और ((-6)(3)=-18) है। परीक्षा में मध्य पद के चिन्ह के अनुसार बड़ा परिमाण वाला चिन्ह चुनें।
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\(3x^2+10x+8\) का सही गुणनखंड रूप कौन-सा है?
Which is the correct factorised form of \(3x^2+10x+8\)?
#quadratic
#factorisation
#area model
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A ((3x+4)(x+2)) / सही रूप
B ((3x+2)(x+4)) / मध्य पद गलत
C ((x+4)(x+2)) / अग्र गुणांक गलत
D ((3x-4)(x-2)) / चिन्ह गलत
Explanation opens after your attempt
Correct Answer
A. ((3x+4)(x+2)) / सही रूप
Step 1
Concept
((3x+4)(x+2)=3x-2 +10x+8). In exams the sum of cross terms gives the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((3x+4)(x+2)) / सही रूप. ((3x+4)(x+2)=3x-2 +10x+8). In exams the sum of cross terms gives the middle term.
Step 3
Exam Tip
((3x+4)(x+2)=3x-2 +10x+8) है। परीक्षा में क्रॉस पदों का योग मध्य पद देता है।
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\(12x^2y-18xy^2\) का सबसे सरल गुणनखंड रूप क्या है?
What is the simplest factorised form of \(12x^2y-18xy^2\)?
#common factor
#gcf
#factorisation
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A (6xy(2x-3y)) / सही रूप
B (6x\(2xy-3y^2\)) / पूरा सरल नहीं
C (3xy(4x-6y)) / सबसे बड़ा समान गुणनखंड नहीं
D (6xy(2x+3y)) / गलत चिन्ह
Explanation opens after your attempt
Correct Answer
A. (6xy(2x-3y)) / सही रूप
Step 1
Concept
The greatest common factor is (6xy). In exams keep the subtraction sign correctly inside the bracket.
Step 2
Why this answer is correct
The correct answer is A. (6xy(2x-3y)) / सही रूप. The greatest common factor is (6xy). In exams keep the subtraction sign correctly inside the bracket.
Step 3
Exam Tip
सबसे बड़ा समान गुणनखंड (6xy) है। परीक्षा में घटाव चिन्ह को कोष्ठक में सही रखें।
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\(a^2+6ab+9b^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(a^2+6ab+9b^2\)?
#perfect square
#identity
#factorisation
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A ((a+3b)2 ) / सही पूर्ण वर्ग
B ((a-3b)2 ) / चिन्ह गलत
C ((a+9b)(a+b)) / मध्य पद गलत
D ((a+6b)(a+3b)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((a+3b)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(9b-2 =(3b)2 ) and \(6ab=2\cdot a\cdot3b\). In exams take the square root of the last term.
Step 2
Why this answer is correct
The correct answer is A. ((a+3b)2 ) / सही पूर्ण वर्ग. (9b-2 =(3b)2 ) and \(6ab=2\cdot a\cdot3b\). In exams take the square root of the last term.
Step 3
Exam Tip
(9b-2 =(3b)2 ) और \(6ab=2\cdot a\cdot3b\) है। परीक्षा में अंतिम पद का वर्गमूल लें।
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\(5x^2-20\) को गुणनखंडित करें।
Factorise \(5x^2-20\).
#common factor
#difference of squares
#factorisation
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A (5(x-2)(x+2)) / सही पूर्ण रूप
B (5\(x^2-20\)) / गलत समान गुणनखंड
C (5(x-4)(x+4)) / गलत वर्गमूल
D ((5x-20)(x+1)) / गलत रूप
Explanation opens after your attempt
Correct Answer
A. (5(x-2)(x+2)) / सही पूर्ण रूप
Step 1
Concept
First take out (5), then \(x^2-4\) is a difference of squares. In exams keep checking after taking the common factor.
Step 2
Why this answer is correct
The correct answer is A. (5(x-2)(x+2)) / सही पूर्ण रूप. First take out (5), then \(x^2-4\) is a difference of squares. In exams keep checking after taking the common factor.
Step 3
Exam Tip
पहले (5) निकालें, फिर \(x^2-4\) वर्गों का अंतर है। परीक्षा में समान गुणनखंड निकालने के बाद भी जांच जारी रखें।
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\(x^2-8x+16\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2-8x+16\)?
#perfect square
#factorisation
#negative middle
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A ((x-4)2 ) / सही पूर्ण वर्ग
B ((x+4)2 ) / गलत चिन्ह
C ((x-8)(x+2)) / गलत गुणनखंड
D ((x-16)2 ) / गलत स्थिर भाग
Explanation opens after your attempt
Correct Answer
A. ((x-4)2 ) / सही पूर्ण वर्ग
Step 1
Concept
\(16=4^2\) and \(-8x=-2\cdot x\cdot4\). In exams half of the middle coefficient gives a clue.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)2 ) / सही पूर्ण वर्ग. \(16=4^2\) and \(-8x=-2\cdot x\cdot4\). In exams half of the middle coefficient gives a clue.
Step 3
Exam Tip
\(16=4^2\) और \(-8x=-2\cdot x\cdot4\) है। परीक्षा में मध्य पद का आधा संकेत देता है।
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(2xy+6y+5x+15) का गुणनखंड रूप कौन-सा है?
Which is the factorised form of (2xy+6y+5x+15)?
#grouping
#common binomial
#factorisation
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A ((2y+5)(x+3)) / सही रूप
B ((2y-5)(x+3)) / चिन्ह गलत
C ((2x+5)(y+3)) / गलत मिलान
D ((x+15)(2y+1)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((2y+5)(x+3)) / सही रूप
Step 1
Concept
The grouping gives (2y(x+3)+5(x+3)). In exams form the second factor after spotting the common bracket.
Step 2
Why this answer is correct
The correct answer is A. ((2y+5)(x+3)) / सही रूप. The grouping gives (2y(x+3)+5(x+3)). In exams form the second factor after spotting the common bracket.
Step 3
Exam Tip
समूह (2y(x+3)+5(x+3)) बनता है। परीक्षा में समान कोष्ठक देखकर दूसरा गुणनखंड बनाएं।
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\(x^2-121\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(x^2-121\)?
#difference of squares
#factorisation
#identity
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A ((x-11)(x+11)) / सही रूप
B ((x-121)(x+121)) / गलत वर्गमूल
C ((x-11)2 ) / पूर्ण वर्ग नहीं
D ((x+11)2 ) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((x-11)(x+11)) / सही रूप
Step 1
Concept
\(121=11^2\), so this is a difference of squares. In exams remember the square root of the number.
Step 2
Why this answer is correct
The correct answer is A. ((x-11)(x+11)) / सही रूप. \(121=11^2\), so this is a difference of squares. In exams remember the square root of the number.
Step 3
Exam Tip
\(121=11^2\), इसलिए यह वर्गों का अंतर है। परीक्षा में संख्या के वर्गमूल को याद रखें।
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\(4x^2+12x+9\) का गुणनखंड रूप चुनें।
Choose the factorised form of \(4x^2+12x+9\).
#perfect square
#identity
#factorisation
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A ((2x+3)2 ) / सही पूर्ण वर्ग
B ((2x-3)2 ) / मध्य पद गलत
C ((4x+9)2 ) / गलत वर्गमूल
D ((2x+9)(2x+1)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((2x+3)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(4x-2 =(2x)2 ), \(9=3^2\), and the middle is (12x). In exams check all three conditions of the identity.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)2 ) / सही पूर्ण वर्ग. (4x-2 =(2x)2 ), \(9=3^2\), and the middle is (12x). In exams check all three conditions of the identity.
Step 3
Exam Tip
(4x-2 =(2x)2 ), \(9=3^2\), और मध्य (12x) है। परीक्षा में पहचान की तीनों शर्तें जांचें।
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\(x^2+4x-21\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2+4x-21\)?
#trinomial
#signed factors
#factorisation
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A ((x+7)(x-3)) / सही रूप
B ((x-7)(x+3)) / मध्य पद गलत
C ((x+1)(x-21)) / मध्य पद गलत
D ((x+4)(x-21)) / गुणनफल गलत
Explanation opens after your attempt
Correct Answer
A. ((x+7)(x-3)) / सही रूप
Step 1
Concept
Here (7+(-3)=4) and (7\cdot(-3)=-21). In exams look for a pair with opposite signs.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)(x-3)) / सही रूप. Here (7+(-3)=4) and (7\cdot(-3)=-21). In exams look for a pair with opposite signs.
Step 3
Exam Tip
(7+(-3)=4) और (7\cdot(-3)=-21) है। परीक्षा में विपरीत चिन्हों वाली जोड़ी देखें।
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\(6x^2+11x+3\) को गुणनखंडित करें।
Factorise \(6x^2+11x+3\).
#quadratic
#factorisation
#split middle
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A ((3x+1)(2x+3)) / सही रूप
B ((6x+1)(x+3)) / मध्य पद गलत
C ((3x+3)(2x+1)) / समान गुणनखंड गलत
D ((3x-1)(2x-3)) / चिन्ह गलत
Explanation opens after your attempt
Correct Answer
A. ((3x+1)(2x+3)) / सही रूप
Step 1
Concept
((3x+1)(2x+3)=6x-2 +11x+3). In exams check both the last term and cross terms.
Step 2
Why this answer is correct
The correct answer is A. ((3x+1)(2x+3)) / सही रूप. ((3x+1)(2x+3)=6x-2 +11x+3). In exams check both the last term and cross terms.
Step 3
Exam Tip
((3x+1)(2x+3)=6x-2 +11x+3) है। परीक्षा में अंतिम पद और क्रॉस पद दोनों जांचें।
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\(a^2b-ab^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(a^2b-ab^2\)?
#common factor
#variables
#factorisation
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A (ab(a-b)) / सही समान गुणनखंड
B (a(a-b)) / (b) छूट गया
C (b(a-b)) / (a) छूट गया
D (ab(a+b)) / गलत चिन्ह
Explanation opens after your attempt
Correct Answer
A. (ab(a-b)) / सही समान गुणनखंड
Step 1
Concept
Both terms have the common factor (ab). In exams identify variables present in every term.
Step 2
Why this answer is correct
The correct answer is A. (ab(a-b)) / सही समान गुणनखंड. Both terms have the common factor (ab). In exams identify variables present in every term.
Step 3
Exam Tip
दोनों पदों में समान गुणनखंड (ab) है। परीक्षा में हर पद में उपस्थित चर पहचानें।
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\(x^2-4x-45\) का सही गुणनखंड रूप कौन-सा है?
Which is the correct factorised form of \(x^2-4x-45\)?
#trinomial
#signed factors
#factorisation
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A ((x-9)(x+5)) / सही रूप
B ((x+9)(x-5)) / मध्य पद गलत
C ((x-15)(x+3)) / मध्य पद गलत
D ((x-45)(x+1)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x-9)(x+5)) / सही रूप
Step 1
Concept
(-9+5=-4) and ((-9)(5)=-45). In exams decide the sign of the larger magnitude from the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((x-9)(x+5)) / सही रूप. (-9+5=-4) and ((-9)(5)=-45). In exams decide the sign of the larger magnitude from the middle term.
Step 3
Exam Tip
(-9+5=-4) और ((-9)(5)=-45) है। परीक्षा में मध्य पद के अनुसार बड़े परिमाण का चिन्ह तय करें।
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(10pq+15p-4q-6) को समूहीकरण से गुणनखंडित करें।
Factorise (10pq+15p-4q-6) by grouping.
#grouping
#negative common factor
#factorisation
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A ((5p-2)(2q+3)) / सही रूप
B ((5p+2)(2q-3)) / चिन्ह गलत
C ((10p-4)(q+6)) / गलत समूह
D ((p-2)(10q+3)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((5p-2)(2q+3)) / सही रूप
Step 1
Concept
The grouping gives (5p(2q+3)-2(2q+3)). In exams you may need to take a negative common factor from the second group.
Step 2
Why this answer is correct
The correct answer is A. ((5p-2)(2q+3)) / सही रूप. The grouping gives (5p(2q+3)-2(2q+3)). In exams you may need to take a negative common factor from the second group.
Step 3
Exam Tip
समूह (5p(2q+3)-2(2q+3)) बनता है। परीक्षा में दूसरे समूह से ऋणात्मक समान गुणनखंड लेना पड़ सकता है।
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\(36x^2-25y^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(36x^2-25y^2\)?
#difference of squares
#factorisation
#identity
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A ((6x-5y)(6x+5y)) / सही वर्गों का अंतर
B ((36x-25y)(36x+25y)) / गलत वर्गमूल
C ((6x-5y)2 ) / पूर्ण वर्ग नहीं
D ((3x-5y)(12x+5y)) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ((6x-5y)(6x+5y)) / सही वर्गों का अंतर
Step 1
Concept
(36x-2 =(6x)2 ) and (25y-2 =(5y)2 ). In exams take square roots of both terms together.
Step 2
Why this answer is correct
The correct answer is A. ((6x-5y)(6x+5y)) / सही वर्गों का अंतर. (36x-2 =(6x)2 ) and (25y-2 =(5y)2 ). In exams take square roots of both terms together.
Step 3
Exam Tip
(36x-2 =(6x)2 ) और (25y-2 =(5y)2 ) है। परीक्षा में दोनों पदों के वर्गमूल साथ लें।
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\(x^2+14x+49\) का गुणनखंड रूप चुनें।
Choose the factorised form of \(x^2+14x+49\).
#perfect square
#trinomial
#factorisation
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A ((x+7)2 ) / सही पूर्ण वर्ग
B ((x-7)2 ) / चिन्ह गलत
C ((x+14)(x+49)) / गलत रूप
D ((x+1)(x+49)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 ) / सही पूर्ण वर्ग
Step 1
Concept
\(49=7^2\) and \(14x=2\cdot x\cdot7\). In exams identify perfect square trinomials quickly.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 ) / सही पूर्ण वर्ग. \(49=7^2\) and \(14x=2\cdot x\cdot7\). In exams identify perfect square trinomials quickly.
Step 3
Exam Tip
\(49=7^2\) और \(14x=2\cdot x\cdot7\) है। परीक्षा में पूर्ण वर्ग त्रिपद तुरंत पहचानें।
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\(3a^2-27b^2\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(3a^2-27b^2\)?
#common factor
#difference of squares
#factorisation
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A (3(a-3b)(a+3b)) / सही रूप
B (3(a-b)(a+b)) / \(27b^2\) नहीं बनेगा
C ((3a-27b)(a+b)) / गलत रूप
D (3(a-9b)2 ) / गलत पहचान
Explanation opens after your attempt
Correct Answer
A. (3(a-3b)(a+3b)) / सही रूप
Step 1
Concept
First take out common (3), then factorise \(a^2-9b^2\). In exams stop only after complete factorisation.
Step 2
Why this answer is correct
The correct answer is A. (3(a-3b)(a+3b)) / सही रूप. First take out common (3), then factorise \(a^2-9b^2\). In exams stop only after complete factorisation.
Step 3
Exam Tip
पहले (3) समान गुणनखंड निकालें, फिर \(a^2-9b^2\) को गुणनखंडित करें। परीक्षा में पूर्ण गुणनखंड तक रुकें।
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\(x^2+x-72\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2+x-72\)?
#trinomial
#signed factors
#factorisation
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A ((x+9)(x-8)) / सही रूप
B ((x-9)(x+8)) / मध्य पद गलत
C ((x+12)(x-6)) / मध्य पद गलत
D ((x+1)(x-72)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((x+9)(x-8)) / सही रूप
Step 1
Concept
Here (9+(-8)=1) and (9\cdot(-8)=-72). In exams read the middle term (1x) carefully.
Step 2
Why this answer is correct
The correct answer is A. ((x+9)(x-8)) / सही रूप. Here (9+(-8)=1) and (9\cdot(-8)=-72). In exams read the middle term (1x) carefully.
Step 3
Exam Tip
(9+(-8)=1) और (9\cdot(-8)=-72) है। परीक्षा में (1x) मध्य पद को भी ध्यान से पढ़ें।
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\(4x^2-12xy+9y^2\) को किस रूप में गुणनखंडित करेंगे?
How will \(4x^2-12xy+9y^2\) be factorised?
#perfect square
#negative middle
#factorisation
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A ((2x-3y)2 ) / सही पूर्ण वर्ग
B ((2x+3y)2 ) / चिन्ह गलत
C ((4x-9y)2 ) / गलत जड़
D ((2x-9y)(2x-y)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((2x-3y)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(4x-2 =(2x)2 ), (9y-2 =(3y)2 ), and the middle term is negative. In exams the sign of the middle term is decisive.
Step 2
Why this answer is correct
The correct answer is A. ((2x-3y)2 ) / सही पूर्ण वर्ग. (4x-2 =(2x)2 ), (9y-2 =(3y)2 ), and the middle term is negative. In exams the sign of the middle term is decisive.
Step 3
Exam Tip
(4x-2 =(2x)2 ), (9y-2 =(3y)2 ) और मध्य पद ऋणात्मक है। परीक्षा में मध्य पद का चिन्ह निर्णायक होता है।
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\(2x^2+13x+15\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(2x^2+13x+15\)?
#quadratic
#factorisation
#cross terms
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A ((2x+3)(x+5)) / सही रूप
B ((2x+5)(x+3)) / मध्य पद गलत
C ((x+3)(x+5)) / अग्र गुणांक गलत
D ((2x-3)(x-5)) / चिन्ह गलत
Explanation opens after your attempt
Correct Answer
A. ((2x+3)(x+5)) / सही रूप
Step 1
Concept
((2x+3)(x+5)=2x-2 +13x+15). In exams add the cross terms (10x) and (3x).
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)(x+5)) / सही रूप. ((2x+3)(x+5)=2x-2 +13x+15). In exams add the cross terms (10x) and (3x).
Step 3
Exam Tip
((2x+3)(x+5)=2x-2 +13x+15) है। परीक्षा में क्रॉस पद (10x) और (3x) जोड़ें।
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(xy+2x+3y+6) को गुणनखंडित करें।
Factorise (xy+2x+3y+6).
#grouping
#common binomial
#factorisation
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A ((x+3)(y+2)) / सही रूप
B ((x+2)(y+3)) / मध्य पदों की अदला-बदली से गलत
C ((x-3)(y-2)) / चिन्ह गलत
D ((xy+6)(x+3)) / गलत रूप
Explanation opens after your attempt
Correct Answer
A. ((x+3)(y+2)) / सही रूप
Step 1
Concept
The grouping gives (x(y+2)+3(y+2)). In exams make the same bracket in both groups.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)(y+2)) / सही रूप. The grouping gives (x(y+2)+3(y+2)). In exams make the same bracket in both groups.
Step 3
Exam Tip
समूह (x(y+2)+3(y+2)) बनता है। परीक्षा में दोनों समूहों में समान कोष्ठक बनाएं।
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\(64a^2+80ab+25b^2\) का गुणनखंड रूप कौन-सा है?
Which is the factorised form of \(64a^2+80ab+25b^2\)?
#perfect square
#identity
#factorisation
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A ((8a+5b)2 ) / सही पूर्ण वर्ग
B ((8a-5b)2 ) / चिन्ह गलत
C ((64a+25b)2 ) / गलत वर्गमूल
D ((8a+25b)(8a+b)) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ((8a+5b)2 ) / सही पूर्ण वर्ग
Step 1
Concept
(64a-2 =(8a)2 ), (25b-2 =(5b)2 ), and \(80ab=2\cdot8a\cdot5b\). In exams match all three conditions of a perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((8a+5b)2 ) / सही पूर्ण वर्ग. (64a-2 =(8a)2 ), (25b-2 =(5b)2 ), and \(80ab=2\cdot8a\cdot5b\). In exams match all three conditions of a perfect square.
Step 3
Exam Tip
(64a-2 =(8a)2 ), (25b-2 =(5b)2 ) और \(80ab=2\cdot8a\cdot5b\) है। परीक्षा में पूर्ण वर्ग की तीनों शर्तें मिलाएं।
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\(3x^2-12\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(3x^2-12\)?
#common factor
#difference of squares
#factorisation
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A (3(x-2)(x+2)) / सही रूप
B (3(x-4)(x+4)) / गलत वर्गमूल
C (3\(x^2-12\)) / पूरा गुणनखंड नहीं
D (3(x-2)2 ) / गलत पहचान
Explanation opens after your attempt
Correct Answer
A. (3(x-2)(x+2)) / सही रूप
Step 1
Concept
First take out common (3), then factorise \(x^2-4\) using difference of squares. In exams apply the identity after taking the common factor.
Step 2
Why this answer is correct
The correct answer is A. (3(x-2)(x+2)) / सही रूप. First take out common (3), then factorise \(x^2-4\) using difference of squares. In exams apply the identity after taking the common factor.
Step 3
Exam Tip
पहले (3) समान गुणनखंड निकालें और फिर \(x^2-4\) को वर्गों के अंतर से गुणनखंडित करें। परीक्षा में समान गुणनखंड के बाद पहचान जरूर लगाएं।
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\(x^2-15x+56\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2-15x+56\)?
#trinomial
#negative factors
#factorisation
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A ( (x-7)(x-8) ) / सही गुणनखंड
B ( (x+7)(x+8) ) / मध्य पद धनात्मक
C ( (x-4)(x-14) ) / मध्य पद गलत
D ( (x-1)(x-56) ) / मध्य पद गलत
Explanation opens after your attempt
Correct Answer
A. ( (x-7)(x-8) ) / सही गुणनखंड
Step 1
Concept
Here (-7+(-8)=-15) and ((-7)(-8)=56). In exams use two negative signs when the constant is positive and the middle term is negative.
Step 2
Why this answer is correct
The correct answer is A. ( (x-7)(x-8) ) / सही गुणनखंड. Here (-7+(-8)=-15) and ((-7)(-8)=56). In exams use two negative signs when the constant is positive and the middle term is negative.
Step 3
Exam Tip
(-7+(-8)=-15) और ((-7)(-8)=56) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद पर दोनों चिन्ह ऋणात्मक रखें।
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(4ab+8a+5b+10) को समूहीकरण से गुणनखंडित करें।
Factorise (4ab+8a+5b+10) by grouping.
#grouping
#common binomial
#factorisation
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A ( (4a+5)(b+2) ) / सही रूप
B ( (4a-5)(b+2) ) / चिन्ह गलत
C ( (a+5)(4b+2) ) / गलत समूह
D ( (4a+10)(b+5) ) / गलत विस्तार
Explanation opens after your attempt
Correct Answer
A. ( (4a+5)(b+2) ) / सही रूप
Step 1
Concept
The grouping gives (4a(b+2)+5(b+2)), and ((b+2)) is common. In exams take out the common bracket when it appears.
Step 2
Why this answer is correct
The correct answer is A. ( (4a+5)(b+2) ) / सही रूप. The grouping gives (4a(b+2)+5(b+2)), and ((b+2)) is common. In exams take out the common bracket when it appears.
Step 3
Exam Tip
समूह (4a(b+2)+5(b+2)) बनता है और ((b+2)) समान गुणनखंड है। परीक्षा में समान कोष्ठक बनने पर उसे बाहर निकालें।
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(6x+9) का गुणनखंड रूप क्या है?
What is the factorised form of (6x+9)?
#factorisation
#common-factor
#algebra
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A (3(2x+3))
B (6(x+9))
C (9(x+6))
D (3(2x+9))
Explanation opens after your attempt
Correct Answer
A. (3(2x+3))
Step 1
Concept
The common factor is (3). In exams, first check the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (3(2x+3)). The common factor is (3). In exams, first check the greatest common factor.
Step 3
Exam Tip
सामान्य गुणनखंड (3) है। परीक्षा में पहले महत्तम सामान्य गुणनखंड देखें।
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\(x^2+5x\) को गुणनखंडित कीजिए।
Factorise \(x^2+5x\).
#factorisation
#common-variable
#class-9
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A (x(x+5))
B (5(x+5))
C (x\(x^2+5\))
D (x+5x)
Explanation opens after your attempt
Correct Answer
A. (x(x+5))
Step 1
Concept
Both terms have (x) common. In exams, take the common variable term outside.
Step 2
Why this answer is correct
The correct answer is A. (x(x+5)). Both terms have (x) common. In exams, take the common variable term outside.
Step 3
Exam Tip
दोनों पदों में (x) सामान्य है। परीक्षा में चर वाले सामान्य पद को बाहर लें।
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\(a^2-b^2\) का सही गुणनखंड कौन-सा है?
Which is the correct factorisation of \(a^2-b^2\)?
#difference-of-squares
#factorisation
#identity
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A ((a-b)(a+b))
B ((a-b)2 )
C ((a+b)2 )
D (a(a-b))
Explanation opens after your attempt
Correct Answer
A. ((a-b)(a+b))
Step 1
Concept
This is a difference of squares. In exams, remember (A-2 -B-2 =(A-B)(A+B)).
Step 2
Why this answer is correct
The correct answer is A. ((a-b)(a+b)). This is a difference of squares. In exams, remember (A-2 -B-2 =(A-B)(A+B)).
Step 3
Exam Tip
यह वर्गों का अंतर है। परीक्षा में (A-2 -B-2 =(A-B)(A+B)) याद रखें।
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\(y^2+10y+25\) का गुणनखंड रूप क्या होगा?
What is the factorised form of \(y^2+10y+25\)?
#perfect-square
#factorisation
#identity
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A ((y+10)(y+25))
B ((y+5)2 )
C ((y-5)2 )
D ((y+2)(y+8))
Explanation opens after your attempt
Correct Answer
B. ((y+5)2 )
Step 1
Concept
\(25=5^2\) and \(10y=2\cdot y\cdot5\). In exams, identify the perfect square trinomial.
Step 2
Why this answer is correct
The correct answer is B. ((y+5)2 ). \(25=5^2\) and \(10y=2\cdot y\cdot5\). In exams, identify the perfect square trinomial.
Step 3
Exam Tip
\(25=5^2\) और \(10y=2\cdot y\cdot5\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।
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\(p^2-12p+36\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(p^2-12p+36\).
#perfect-square
#minus-square
#factorisation
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A ((p+6)2 )
B ((p-6)2 )
C ((p-12)(p+3))
D ((p-3)(p-12))
Explanation opens after your attempt
Correct Answer
B. ((p-6)2 )
Step 1
Concept
\(36=6^2\) and the middle term is negative. In exams, use the sign to choose ((p-6)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((p-6)2 ). \(36=6^2\) and the middle term is negative. In exams, use the sign to choose ((p-6)2 ).
Step 3
Exam Tip
\(36=6^2\) और मध्य पद ऋणात्मक है। परीक्षा में चिह्न देखकर ((p-6)2 ) चुनें।
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\(x^2+8x+15\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+8x+15\)?
#quadratic-factorisation
#sum-product
#algebra
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A ((x+1)(x+15))
B ((x+3)(x+5))
C ((x-3)(x-5))
D ((x+2)(x+6))
Explanation opens after your attempt
Correct Answer
B. ((x+3)(x+5))
Step 1
Concept
(3+5=8) and \(3\cdot5=15\). In exams, match both sum and product.
Step 2
Why this answer is correct
The correct answer is B. ((x+3)(x+5)). (3+5=8) and \(3\cdot5=15\). In exams, match both sum and product.
Step 3
Exam Tip
(3+5=8) और \(3\cdot5=15\) है। परीक्षा में योग और गुणनफल दोनों मिलाएँ।
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\(x^2+11x+30\) के गुणनखंड कौन-से हैं?
What are the factors of \(x^2+11x+30\)?
#factor-pair
#quadratic
#medium
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A ((x+5)(x+6))
B ((x+3)(x+10))
C ((x+2)(x+15))
D ((x-5)(x-6))
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x+6))
Step 1
Concept
(5+6=11) and \(5\cdot6=30\). In exams, test factor pairs of the constant term.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x+6)). (5+6=11) and \(5\cdot6=30\). In exams, test factor pairs of the constant term.
Step 3
Exam Tip
(5+6=11) और \(5\cdot6=30\) है। परीक्षा में स्थिर पद के गुणनखंडों की जोड़ी जाँचें।
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\(m^2-m-20\) को गुणनखंडित कीजिए।
Factorise \(m^2-m-20\).
#signed-factors
#quadratic-factorisation
#algebra
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A ((m-5 )(m+4))
B ((m+5)(m+4))
C ((m-4 )(m-5 ))
D ((m+5)(m-4 ))
Explanation opens after your attempt
Correct Answer
A. ((m-5 )(m+4))
Step 1
Concept
(-5+4=-1) and \(-5\cdot4=-20\). In exams, use opposite signs for a negative constant term.
Step 2
Why this answer is correct
The correct answer is A. ((m-5 )(m+4)). (-5+4=-1) and \(-5\cdot4=-20\). In exams, use opposite signs for a negative constant term.
Step 3
Exam Tip
(-5+4=-1) और \(-5\cdot4=-20\) है। परीक्षा में ऋणात्मक स्थिर पद के लिए विपरीत चिह्न लें।
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\(a^2-7a+12\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(a^2-7a+12\)?
#quadratic
#factorisation
#signs
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A ((a+3)(a+4))
B ((a-3)(a-4))
C ((a-2)(a-6))
D ((a+2)(a+6))
Explanation opens after your attempt
Correct Answer
B. ((a-3)(a-4))
Step 1
Concept
(-3-4=-7) and ((-3)(-4)=12). In exams, for positive constant and negative middle term, use both negative signs.
Step 2
Why this answer is correct
The correct answer is B. ((a-3)(a-4)). (-3-4=-7) and ((-3)(-4)=12). In exams, for positive constant and negative middle term, use both negative signs.
Step 3
Exam Tip
(-3-4=-7) और ((-3)(-4)=12) है। परीक्षा में धनात्मक स्थिर और ऋणात्मक मध्य पद पर दोनों चिह्न ऋण रखें।
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\(2x^2+7x+3\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(2x^2+7x+3\).
#middle-term-split
#factorisation
#quadratic
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A ((2x+3)(x+1))
B ((2x+1)(x+3))
C ((x+2)(x+3))
D ((2x-1)(x-3))
Explanation opens after your attempt
Correct Answer
B. ((2x+1)(x+3))
Step 1
Concept
Expanding gives \(2x^2+6x+x+3=2x^2+7x+3\). In exams, verify by multiplication.
Step 2
Why this answer is correct
The correct answer is B. ((2x+1)(x+3)). Expanding gives \(2x^2+6x+x+3=2x^2+7x+3\). In exams, verify by multiplication.
Step 3
Exam Tip
विस्तार करने पर \(2x^2+6x+x+3=2x^2+7x+3\) मिलता है। परीक्षा में गुणा करके उत्तर जाँचें।
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\(3y^2+10y+8\) के गुणनखंड क्या होंगे?
What will be the factors of \(3y^2+10y+8\)?
#quadratic-factorisation
#expansion-check
#algebra
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A ((3y+4)(y+2))
B ((3y+2)(y+4))
C ((y+4)(y+6))
D ((3y-4)(y-2))
Explanation opens after your attempt
Correct Answer
A. ((3y+4)(y+2))
Step 1
Concept
((3y+4)(y+2)) gives \(3y^2+6y+4y+8\). In exams, check by adding middle terms.
Step 2
Why this answer is correct
The correct answer is A. ((3y+4)(y+2)). ((3y+4)(y+2)) gives \(3y^2+6y+4y+8\). In exams, check by adding middle terms.
Step 3
Exam Tip
((3y+4)(y+2)) से \(3y^2+6y+4y+8\) मिलता है। परीक्षा में मध्य पद जोड़कर देखें।
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\(4p^2-9\) का सही गुणनखंड कौन-सा है?
Which is the correct factorisation of \(4p^2-9\)?
#difference-of-squares
#factorisation
#identity
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A ((4p-3)(p+3))
B ((2p-3)(2p+3))
C ((2p-9)(2p+1))
D ((2p-3)2 )
Explanation opens after your attempt
Correct Answer
B. ((2p-3)(2p+3))
Step 1
Concept
(4p-2 =(2p)2 ) and \(9=3^2\). In exams, apply the difference of squares formula.
Step 2
Why this answer is correct
The correct answer is B. ((2p-3)(2p+3)). (4p-2 =(2p)2 ) and \(9=3^2\). In exams, apply the difference of squares formula.
Step 3
Exam Tip
(4p-2 =(2p)2 ) और \(9=3^2\) है। परीक्षा में वर्गों के अंतर का सूत्र लगाएँ।
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\(9a^2-25b^2\) को गुणनखंडित कीजिए।
Factorise \(9a^2-25b^2\).
#difference-of-squares
#two-variables
#factorisation
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A ((9a-25b)(a+b))
B ((3a-5b)(3a+5b))
C ((3a-5b)2 )
D ((9a+25b)(9a-25b))
Explanation opens after your attempt
Correct Answer
B. ((3a-5b)(3a+5b))
Step 1
Concept
(9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). In exams, take square roots of both terms.
Step 2
Why this answer is correct
The correct answer is B. ((3a-5b)(3a+5b)). (9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). In exams, take square roots of both terms.
Step 3
Exam Tip
(9a-2 =(3a)2 ) और (25b-2 =(5b)2 ) है। परीक्षा में दोनों पदों का वर्गमूल लें।
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\(4x^2+12x+9\) का गुणनखंड रूप क्या होगा?
What is the factorised form of \(4x^2+12x+9\)?
#perfect-square
#coefficient
#factorisation
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A ((2x+3)2 )
B ((4x+3)2 )
C ((2x-3)2 )
D ((x+6)(x+6))
Explanation opens after your attempt
Correct Answer
A. ((2x+3)2 )
Step 1
Concept
(4x-2 =(2x)2 ), \(9=3^2\), and \(12x=2\cdot2x\cdot3\). In exams, check all three conditions of a perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)2 ). (4x-2 =(2x)2 ), \(9=3^2\), and \(12x=2\cdot2x\cdot3\). In exams, check all three conditions of a perfect square.
Step 3
Exam Tip
(4x-2 =(2x)2 ), \(9=3^2\) और \(12x=2\cdot2x\cdot3\) है। परीक्षा में पूर्ण वर्ग की तीनों शर्तें जाँचें।
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\(25r^2-30r+9\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(25r^2-30r+9\).
#perfect-square
#negative-middle
#factorisation
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A ((5r+3)2 )
B ((25r-3)2 )
C ((5r-3)2 )
D ((5r-9)(5r-1))
Explanation opens after your attempt
Correct Answer
C. ((5r-3)2 )
Step 1
Concept
(25r-2 =(5r)2 ) and \(9=3^2\), with a negative middle term. In exams, identify ((A-B)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((5r-3)2 ). (25r-2 =(5r)2 ) and \(9=3^2\), with a negative middle term. In exams, identify ((A-B)2 ).
Step 3
Exam Tip
(25r-2 =(5r)2 ) और \(9=3^2\), मध्य पद ऋणात्मक है। परीक्षा में ((A-B)2 ) पहचानें।
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(ax+ay+bx+by) का गुणनखंड रूप क्या है?
What is the factorised form of (ax+ay+bx+by)?
#grouping
#factorisation
#algebraic-identities
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A ((a+b)(x+y))
B ((a+x)(b+y))
C ((a+y)(b+x))
D (ab(x+y))
Explanation opens after your attempt
Correct Answer
A. ((a+b)(x+y))
Step 1
Concept
Grouping gives (a(x+y)+b(x+y)). In exams, take the common binomial outside.
Step 2
Why this answer is correct
The correct answer is A. ((a+b)(x+y)). Grouping gives (a(x+y)+b(x+y)). In exams, take the common binomial outside.
Step 3
Exam Tip
समूहन से (a(x+y)+b(x+y)) मिलता है। परीक्षा में समान द्विपद को सामान्य लें।
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(px+qx+py+qy) को समूहन से गुणनखंडित कीजिए।
Factorise (px+qx+py+qy) by grouping.
#factorisation
#grouping
#common-binomial
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A ((p+q)(x+y))
B ((p+x)(q+y))
C ((p+y)(q+x))
D (pq(x+y))
Explanation opens after your attempt
Correct Answer
A. ((p+q)(x+y))
Step 1
Concept
It can be written as (x(p+q)+y(p+q)). In exams, group the first two and last two terms correctly.
Step 2
Why this answer is correct
The correct answer is A. ((p+q)(x+y)). It can be written as (x(p+q)+y(p+q)). In exams, group the first two and last two terms correctly.
Step 3
Exam Tip
इसे (x(p+q)+y(p+q)) लिखा जा सकता है। परीक्षा में पहले दो और अंतिम दो पदों को सही समूह में रखें।
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\(x^2+9x+20\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+9x+20\).
#quadratic-factorisation
#sum-product
#practice
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A ((x+4)(x+5))
B ((x+2)(x+10))
C ((x+1)(x+20))
D ((x-4)(x-5))
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x+5))
Step 1
Concept
(4+5=9) and \(4\cdot5=20\). In exams, do not quickly choose (2) and (10).
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x+5)). (4+5=9) and \(4\cdot5=20\). In exams, do not quickly choose (2) and (10).
Step 3
Exam Tip
(4+5=9) और \(4\cdot5=20\) है। परीक्षा में जल्दीबाजी में (2) और (10) न चुनें।
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\(z^2-13z+40\) के गुणनखंड क्या हैं?
What are the factors of \(z^2-13z+40\)?
#quadratic
#negative-middle
#factorisation
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A ((z-5)(z-8))
B ((z+5)(z+8))
C ((z-4)(z-10))
D ((z+4)(z+10))
Explanation opens after your attempt
Correct Answer
A. ((z-5)(z-8))
Step 1
Concept
(-5-8=-13) and ((-5)(-8)=40). In exams, choose both negative factors.
Step 2
Why this answer is correct
The correct answer is A. ((z-5)(z-8)). (-5-8=-13) and ((-5)(-8)=40). In exams, choose both negative factors.
Step 3
Exam Tip
(-5-8=-13) और ((-5)(-8)=40) है। परीक्षा में दोनों ऋणात्मक गुणनखंड चुनें।
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\(u^2+u-42\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(u^2+u-42\)?
#signed-factorisation
#quadratic
#class-9
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A ((u+7)(u-6))
B ((u-7)(u+6))
C ((u+3)(u-14))
D ((u+42)(u-1))
Explanation opens after your attempt
Correct Answer
A. ((u+7)(u-6))
Step 1
Concept
(7-6=1) and (7\cdot(-6)=-42). In exams, use the middle-term sign to decide the larger number's sign.
Step 2
Why this answer is correct
The correct answer is A. ((u+7)(u-6)). (7-6=1) and (7\cdot(-6)=-42). In exams, use the middle-term sign to decide the larger number's sign.
Step 3
Exam Tip
(7-6=1) और (7\cdot(-6)=-42) है। परीक्षा में मध्य पद के चिह्न से बड़ी संख्या का चिह्न तय करें।
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\(k^2-2k-35\) को गुणनखंडित कीजिए।
Factorise \(k^2-2k-35\).
#quadratic-factorisation
#signs
#practice
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A ((k+5)(k-7))
B ((k-5)(k+7))
C ((k-35)(k+1))
D ((k-2)(k-35))
Explanation opens after your attempt
Correct Answer
A. ((k+5)(k-7))
Step 1
Concept
(5-7=-2) and (5\cdot(-7)=-35). In exams, match both product and sum.
Step 2
Why this answer is correct
The correct answer is A. ((k+5)(k-7)). (5-7=-2) and (5\cdot(-7)=-35). In exams, match both product and sum.
Step 3
Exam Tip
(5-7=-2) और (5\cdot(-7)=-35) है। परीक्षा में गुणनफल और योग दोनों मिलाएँ।
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\(12x^2y+18xy^2\) का सामान्य गुणनखंड निकालकर रूप क्या होगा?
By taking the common factor, what is the form of \(12x^2y+18xy^2\)?
#common-factor
#two-variables
#factorisation
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A (6xy(2x+3y))
B (6x\(2xy+3y^2\))
C (3xy(4x+6y))
D (12xy(x+y))
Explanation opens after your attempt
Correct Answer
A. (6xy(2x+3y))
Step 1
Concept
The greatest common factor is (6xy). In exams, take the common part of both numbers and variables.
Step 2
Why this answer is correct
The correct answer is A. (6xy(2x+3y)). The greatest common factor is (6xy). In exams, take the common part of both numbers and variables.
Step 3
Exam Tip
महत्तम सामान्य गुणनखंड (6xy) है। परीक्षा में संख्या और चर दोनों का सामान्य भाग लें।
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\(15a^2b-10ab^2\) का पूर्ण सामान्य गुणनखंड रूप क्या है?
What is the complete common-factor form of \(15a^2b-10ab^2\)?
#common-factor
#monomials
#factorisation
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A (5ab(3a-2b))
B (5a\(3ab-2b^2\))
C (10ab(a-b))
D (15ab(a-2b))
Explanation opens after your attempt
Correct Answer
A. (5ab(3a-2b))
Step 1
Concept
Both terms have (5ab) common. In exams, after taking the greatest common factor, check the bracket.
Step 2
Why this answer is correct
The correct answer is A. (5ab(3a-2b)). Both terms have (5ab) common. In exams, after taking the greatest common factor, check the bracket.
Step 3
Exam Tip
दोनों पदों में (5ab) सामान्य है। परीक्षा में महत्तम सामान्य गुणनखंड निकालने के बाद कोष्ठक जाँचें।
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\(16x^2-24xy\) को गुणनखंडों में लिखिए।
Write \(16x^2-24xy\) in factors.
#common-factor
#algebraic-expression
#medium
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A (8x(2x-3y))
B (4x(4x-6y))
C (8xy(2x-3))
D (16x(x-y))
Explanation opens after your attempt
Correct Answer
A. (8x(2x-3y))
Step 1
Concept
The greatest common factor is (8x). In exams, multiply the bracket back to check.
Step 2
Why this answer is correct
The correct answer is A. (8x(2x-3y)). The greatest common factor is (8x). In exams, multiply the bracket back to check.
Step 3
Exam Tip
महत्तम सामान्य गुणनखंड (8x) है। परीक्षा में अंदर के पदों को फिर से गुणा करके जाँचें।
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\(x^2+2xy+y^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+2xy+y^2\)?
#perfect-square
#two-variables
#factorisation
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A ((x+y)2 )
B ((x-y)2 )
C ((x+y)(x-y))
D (x(x+2y))
Explanation opens after your attempt
Correct Answer
A. ((x+y)2 )
Step 1
Concept
This is a perfect square of (x) and (y). In exams, identify (2xy) as the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((x+y)2 ). This is a perfect square of (x) and (y). In exams, identify (2xy) as the middle term.
Step 3
Exam Tip
यह (x) और (y) का पूर्ण वर्ग है। परीक्षा में (2xy) को मध्य पद के रूप में पहचानें।
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\(x^2-2xy+y^2\) को गुणनखंडित कीजिए।
Factorise \(x^2-2xy+y^2\).
#perfect-square
#minus-square
#two-variables
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? Hint Small clue
A ((x+y)2 )
B ((x-y)2 )
C ((x-y)(x+y))
D (y(x-y))
Explanation opens after your attempt
Correct Answer
B. ((x-y)2 )
Step 1
Concept
This is the perfect square of the difference of (x) and (y). In exams, identify ((x-y)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. ((x-y)2 ). This is the perfect square of the difference of (x) and (y). In exams, identify ((x-y)2 ) from the negative middle term.
Step 3
Exam Tip
यह (x) और (y) के अंतर का पूर्ण वर्ग है। परीक्षा में ऋणात्मक मध्य पद से ((x-y)2 ) पहचानें।
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\(36m^2-49n^2\) का सही गुणनखंड कौन-सा है?
Which is the correct factorisation of \(36m^2-49n^2\)?
#difference-of-squares
#two-variables
#identity
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A ((6m-7n)(6m+7n))
B ((36m-49n)(m+n))
C ((6m-7n)2 )
D ((6m+49n)(6m-7n))
Explanation opens after your attempt
Correct Answer
A. ((6m-7n)(6m+7n))
Step 1
Concept
(36m-2 =(6m)2 ) and (49n-2 =(7n)2 ). In exams, write the difference of two squares.
Step 2
Why this answer is correct
The correct answer is A. ((6m-7n)(6m+7n)). (36m-2 =(6m)2 ) and (49n-2 =(7n)2 ). In exams, write the difference of two squares.
Step 3
Exam Tip
(36m-2 =(6m)2 ) और (49n-2 =(7n)2 ) है। परीक्षा में दोनों वर्गों का अंतर लिखें।
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\(49x^2+14xy+y^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(49x^2+14xy+y^2\)?
#perfect-square
#two-variables
#factorisation
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? Hint Small clue
A ((7x+y)2 )
B ((7x-y)2 )
C ((49x+y)2 )
D ((7x+y)(7x-y))
Explanation opens after your attempt
Correct Answer
A. ((7x+y)2 )
Step 1
Concept
(49x-2 =(7x)2 ) and the middle term is \(2\cdot7x\cdot y\). In exams, check square roots of first and last terms.
Step 2
Why this answer is correct
The correct answer is A. ((7x+y)2 ). (49x-2 =(7x)2 ) and the middle term is \(2\cdot7x\cdot y\). In exams, check square roots of first and last terms.
Step 3
Exam Tip
(49x-2 =(7x)2 ) और मध्य पद \(2\cdot7x\cdot y\) है। परीक्षा में पहले और अंतिम पद के वर्गमूल देखें।
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\(81a^2-18ab+b^2\) को गुणनखंडित कीजिए।
Factorise \(81a^2-18ab+b^2\).
#minus-perfect-square
#two-variables
#identity
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? Hint Small clue
A ((9a+b)2 )
B ((9a-b)2 )
C ((81a-b)2 )
D ((9a-b)(9a+b))
Explanation opens after your attempt
Correct Answer
B. ((9a-b)2 )
Step 1
Concept
(81a-2 =(9a)2 ) and the middle term is \(-2\cdot9a\cdot b\). In exams, keep the negative sign carefully.
Step 2
Why this answer is correct
The correct answer is B. ((9a-b)2 ). (81a-2 =(9a)2 ) and the middle term is \(-2\cdot9a\cdot b\). In exams, keep the negative sign carefully.
Step 3
Exam Tip
(81a-2 =(9a)2 ) और मध्य पद \(-2\cdot9a\cdot b\) है। परीक्षा में ऋण चिह्न को ध्यान से रखें।
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\(2x^2+5x+2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(2x^2+5x+2\).
#quadratic-factorisation
#middle-term
#practice
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A ((2x+1)(x+2))
B ((2x+2)(x+1))
C ((x+1)(x+4))
D ((2x-1)(x-2))
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x+2))
Step 1
Concept
Expansion gives \(2x^2+4x+x+2\). In exams, confirm the middle term (5x).
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x+2)). Expansion gives \(2x^2+4x+x+2\). In exams, confirm the middle term (5x).
Step 3
Exam Tip
विस्तार से \(2x^2+4x+x+2\) मिलता है। परीक्षा में मध्य पद (5x) की पुष्टि करें।
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\(3x^2+11x+6\) के गुणनखंड क्या होंगे?
What will be the factors of \(3x^2+11x+6\)?
#quadratic
#expansion-check
#factorisation
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A ((3x+2)(x+3))
B ((3x+1)(x+6))
C ((x+2)(3x+3))
D ((3x-2)(x-3))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(x+3))
Step 1
Concept
((3x+2)(x+3)) gives \(3x^2+9x+2x+6\). In exams, check (9x+2x=11x).
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(x+3)). ((3x+2)(x+3)) gives \(3x^2+9x+2x+6\). In exams, check (9x+2x=11x).
Step 3
Exam Tip
((3x+2)(x+3)) से \(3x^2+9x+2x+6\) मिलता है। परीक्षा में (9x+2x=11x) जाँचें।
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\(5x^2+16x+3\) को गुणनखंडों में लिखिए।
Write \(5x^2+16x+3\) in factors.
#factorisation
#quadratic
#coefficient
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? Hint Small clue
A ((5x+1)(x+3))
B ((5x+3)(x+1))
C ((x+5)(x+3))
D ((5x-1)(x-3))
Explanation opens after your attempt
Correct Answer
A. ((5x+1)(x+3))
Step 1
Concept
((5x+1)(x+3)) has middle term (15x+x=16x). In exams, place the larger coefficient correctly.
Step 2
Why this answer is correct
The correct answer is A. ((5x+1)(x+3)). ((5x+1)(x+3)) has middle term (15x+x=16x). In exams, place the larger coefficient correctly.
Step 3
Exam Tip
((5x+1)(x+3)) में मध्य पद (15x+x=16x) है। परीक्षा में बड़ा गुणांक सही जगह रखें।
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\(6x^2+13x+6\) का गुणनखंड रूप क्या है?
What is the factorised form of \(6x^2+13x+6\)?
#quadratic-factorisation
#coefficient
#medium
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A ((2x+3)(3x+2))
B ((6x+3)(x+2))
C ((3x+3)(2x+2))
D ((2x-3)(3x-2))
Explanation opens after your attempt
Correct Answer
A. ((2x+3)(3x+2))
Step 1
Concept
((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). In exams, check the sum of middle terms.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)(3x+2)). ((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). In exams, check the sum of middle terms.
Step 3
Exam Tip
((2x+3)(3x+2)) से \(6x^2+4x+9x+6\) मिलता है। परीक्षा में मध्य पदों का योग देखें।
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\(2a^2-a-15\) का सही गुणनखंड कौन-सा है?
Which is the correct factorisation of \(2a^2-a-15\)?
#signed-quadratic
#factorisation
#algebra
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A ((2a+5)(a-3))
B ((2a-5)(a+3))
C ((a+5)(2a-3))
D ((2a-1)(a-15))
Explanation opens after your attempt
Correct Answer
A. ((2a+5)(a-3))
Step 1
Concept
Expansion gives \(2a^2-6a+5a-15=2a^2-a-15\). In exams, use unlike signs for a negative constant term.
Step 2
Why this answer is correct
The correct answer is A. ((2a+5)(a-3)). Expansion gives \(2a^2-6a+5a-15=2a^2-a-15\). In exams, use unlike signs for a negative constant term.
Step 3
Exam Tip
विस्तार से \(2a^2-6a+5a-15=2a^2-a-15\) मिलता है। परीक्षा में ऋणात्मक स्थिर पद के लिए चिह्न अलग रखें।
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\(3b^2-2b-8\) को गुणनखंडित कीजिए।
Factorise \(3b^2-2b-8\).
#quadratic-factorisation
#signs
#practice
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A ((3b+4)(b-2))
B ((3b-4)(b+2))
C ((b-4)(3b+2))
D ((3b-2)(b+4))
Explanation opens after your attempt
Correct Answer
A. ((3b+4)(b-2))
Step 1
Concept
((3b+4)(b-2)) gives \(3b^2-6b+4b-8\). In exams, check (-6b+4b=-2b).
Step 2
Why this answer is correct
The correct answer is A. ((3b+4)(b-2)). ((3b+4)(b-2)) gives \(3b^2-6b+4b-8\). In exams, check (-6b+4b=-2b).
Step 3
Exam Tip
((3b+4)(b-2)) से \(3b^2-6b+4b-8\) मिलता है। परीक्षा में (-6b+4b=-2b) जाँचें।
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\(4x^2-12x+9\) के गुणनखंड क्या होंगे?
What are the factors of \(4x^2-12x+9\)?
#perfect-square
#minus-square
#factorisation
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? Hint Small clue
A ((2x+3)2 )
B ((2x-3)2 )
C ((4x-9)(x-1))
D ((2x-3)(2x+3))
Explanation opens after your attempt
Correct Answer
B. ((2x-3)2 )
Step 1
Concept
This is the perfect square of the difference of (2x) and (3). In exams, check \(-12x=-2\cdot2x\cdot3\).
Step 2
Why this answer is correct
The correct answer is B. ((2x-3)2 ). This is the perfect square of the difference of (2x) and (3). In exams, check \(-12x=-2\cdot2x\cdot3\).
Step 3
Exam Tip
यह (2x) और (3) के अंतर का पूर्ण वर्ग है। परीक्षा में \(-12x=-2\cdot2x\cdot3\) देखें।
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\(x^2+14x+49\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+14x+49\)?
#perfect-square
#quadratic
#factorisation
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A ((x+7)2 )
B ((x-7)2 )
C ((x+14)(x+49))
D ((x+5)(x+9))
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 )
Step 1
Concept
\(49=7^2\) and \(14x=2\cdot x\cdot7\). In exams, identify the perfect square trinomial quickly.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 ). \(49=7^2\) and \(14x=2\cdot x\cdot7\). In exams, identify the perfect square trinomial quickly.
Step 3
Exam Tip
\(49=7^2\) और \(14x=2\cdot x\cdot7\) है। परीक्षा में पूर्ण वर्ग त्रिपद तुरंत पहचानें।
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\(x^2-16x+64\) को गुणनखंडों में लिखिए।
Write \(x^2-16x+64\) in factors.
#perfect-square
#negative-middle
#identity
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A ((x-8)2 )
B ((x+8)2 )
C ((x-4)(x-16))
D ((x+4)(x+16))
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 )
Step 1
Concept
\(64=8^2\) and the middle term is (-16x). In exams, choose ((x-8)2 ) based on the sign.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 ). \(64=8^2\) and the middle term is (-16x). In exams, choose ((x-8)2 ) based on the sign.
Step 3
Exam Tip
\(64=8^2\) और मध्य पद (-16x) है। परीक्षा में चिह्न के आधार पर ((x-8)2 ) चुनें।
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(7x+7y+2x+2y) का गुणनखंड रूप क्या होगा?
What will be the factorised form of (7x+7y+2x+2y)?
#grouping
#common-binomial
#factorisation
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A ((7+2)(x+y))
B ((7x+2)(y+1))
C ((7+y)(x+2))
D (7(x+y))
Explanation opens after your attempt
Correct Answer
A. ((7+2)(x+y))
Step 1
Concept
Grouping gives (7(x+y)+2(x+y)). In exams, take the common binomial outside.
Step 2
Why this answer is correct
The correct answer is A. ((7+2)(x+y)). Grouping gives (7(x+y)+2(x+y)). In exams, take the common binomial outside.
Step 3
Exam Tip
समूहन से (7(x+y)+2(x+y)) मिलता है। परीक्षा में समान द्विपद को सामान्य लें।
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(3a+3b+xa+xb) को गुणनखंडित कीजिए।
Factorise (3a+3b+xa+xb).
#factorisation
#grouping
#algebraic-identities
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? Hint Small clue
A ((3+x)(a+b))
B ((3+a)(x+b))
C ((3+b)(x+a))
D (3x(a+b))
Explanation opens after your attempt
Correct Answer
A. ((3+x)(a+b))
Step 1
Concept
It can be written as (3(a+b)+x(a+b)). In exams, identify the common bracket.
Step 2
Why this answer is correct
The correct answer is A. ((3+x)(a+b)). It can be written as (3(a+b)+x(a+b)). In exams, identify the common bracket.
Step 3
Exam Tip
इसे (3(a+b)+x(a+b)) लिखा जा सकता है। परीक्षा में समान कोष्ठक पहचानें।
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\(x^2-81\) का सही गुणनखंड क्या है?
What is the correct factorisation of \(x^2-81\)?
#difference-of-squares
#factorisation
#class-9
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A ((x-9)(x+9))
B ((x-81)(x+1))
C ((x-9)2 )
D ((x+9)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-9)(x+9))
Step 1
Concept
\(81=9^2\), so it is a difference of squares. In exams, write ((x-9)(x+9)).
Step 2
Why this answer is correct
The correct answer is A. ((x-9)(x+9)). \(81=9^2\), so it is a difference of squares. In exams, write ((x-9)(x+9)).
Step 3
Exam Tip
\(81=9^2\) है इसलिए यह वर्गों का अंतर है। परीक्षा में ((x-9)(x+9)) लिखें।
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\(100a^2-b^2\) को गुणनखंडित कीजिए।
Factorise \(100a^2-b^2\).
#difference-of-squares
#two-variables
#identity
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? Hint Small clue
A ((10a-b)(10a+b))
B ((100a-b)(a+b))
C ((10a-b)2 )
D ((100a+b)(100a-b))
Explanation opens after your attempt
Correct Answer
A. ((10a-b)(10a+b))
Step 1
Concept
(100a-2 =(10a)2 ), and \(b^2\) is already a square. In exams, take square roots and write conjugate factors.
Step 2
Why this answer is correct
The correct answer is A. ((10a-b)(10a+b)). (100a-2 =(10a)2 ), and \(b^2\) is already a square. In exams, take square roots and write conjugate factors.
Step 3
Exam Tip
(100a-2 =(10a)2 ) है और \(b^2\) पहले से वर्ग है। परीक्षा में वर्गमूल लेकर संयुग्म गुणनखंड लिखें।
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\(x^2+3x-28\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+3x-28\).
#quadratic-factorisation
#signed-factors
#medium
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A ((x+7)(x-4))
B ((x-7)(x+4))
C ((x+14)(x-2))
D ((x+28)(x-1))
Explanation opens after your attempt
Correct Answer
A. ((x+7)(x-4))
Step 1
Concept
(7-4=3) and (7\cdot(-4)=-28). In exams, keep the larger number's sign like the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)(x-4)). (7-4=3) and (7\cdot(-4)=-28). In exams, keep the larger number's sign like the middle term.
Step 3
Exam Tip
(7-4=3) और (7\cdot(-4)=-28) है। परीक्षा में बड़ी संख्या का चिह्न मध्य पद जैसा रखें।
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\(x^2-4x-45\) के गुणनखंड क्या हैं?
What are the factors of \(x^2-4x-45\)?
#quadratic
#negative-constant
#factorisation
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A ((x+5)(x-9))
B ((x-5)(x+9))
C ((x-15)(x+3))
D ((x+45)(x-1))
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x-9))
Step 1
Concept
(5-9=-4) and (5\cdot(-9)=-45). In exams, use unlike signs when the product is negative.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x-9)). (5-9=-4) and (5\cdot(-9)=-45). In exams, use unlike signs when the product is negative.
Step 3
Exam Tip
(5-9=-4) और (5\cdot(-9)=-45) है। परीक्षा में गुणनफल ऋणात्मक हो तो चिह्न अलग रखें।
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\(2x^2+9x+10\) का सही गुणनखंड कौन-सा है?
Which is the correct factorisation of \(2x^2+9x+10\)?
#coefficient-quadratic
#factorisation
#algebra
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? Hint Small clue
A ((2x+5)(x+2))
B ((2x+1)(x+10))
C ((x+5)(x+4))
D ((2x-5)(x-2))
Explanation opens after your attempt
Correct Answer
A. ((2x+5)(x+2))
Step 1
Concept
((2x+5)(x+2)) gives \(2x^2+4x+5x+10\). In exams, check the middle term (9x).
Step 2
Why this answer is correct
The correct answer is A. ((2x+5)(x+2)). ((2x+5)(x+2)) gives \(2x^2+4x+5x+10\). In exams, check the middle term (9x).
Step 3
Exam Tip
((2x+5)(x+2)) से \(2x^2+4x+5x+10\) मिलता है। परीक्षा में मध्य पद (9x) जाँचें।
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\(4y^2+4y+1\) को गुणनखंडित कीजिए।
Factorise \(4y^2+4y+1\).
#perfect-square
#coefficient
#factorisation
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? Hint Small clue
A ((2y+1)2 )
B ((4y+1)2 )
C ((2y-1)2 )
D ((y+1)(4y+1))
Explanation opens after your attempt
Correct Answer
A. ((2y+1)2 )
Step 1
Concept
(4y-2 =(2y)2 ) and \(1=1^2\). In exams, confirm using \(2\cdot2y\cdot1=4y\).
Step 2
Why this answer is correct
The correct answer is A. ((2y+1)2 ). (4y-2 =(2y)2 ) and \(1=1^2\). In exams, confirm using \(2\cdot2y\cdot1=4y\).
Step 3
Exam Tip
(4y-2 =(2y)2 ) और \(1=1^2\) है। परीक्षा में मध्य पद \(2\cdot2y\cdot1=4y\) से पुष्टि करें।
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\(9p^2+24p+16\) का गुणनखंड रूप क्या है?
What is the factorised form of \(9p^2+24p+16\)?
#perfect-square
#identity
#factorisation
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? Hint Small clue
A ((3p+4)2 )
B ((9p+4)2 )
C ((3p-4)2 )
D ((p+8)(9p+2))
Explanation opens after your attempt
Correct Answer
A. ((3p+4)2 )
Step 1
Concept
(9p-2 =(3p)2 ), \(16=4^2\), and \(24p=2\cdot3p\cdot4\). In exams, identify the perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((3p+4)2 ). (9p-2 =(3p)2 ), \(16=4^2\), and \(24p=2\cdot3p\cdot4\). In exams, identify the perfect square.
Step 3
Exam Tip
(9p-2 =(3p)2 ), \(16=4^2\) और \(24p=2\cdot3p\cdot4\) है। परीक्षा में पूर्ण वर्ग की पहचान करें।
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\(x^2-25y^2\) को गुणनखंडों में लिखिए।
Write \(x^2-25y^2\) in factors.
#difference-of-squares
#two-variables
#factorisation
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? Hint Small clue
A ((x-5y)(x+5y))
B ((x-25y)(x+y))
C ((x-5y)2 )
D ((x+5y)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-5y)(x+5y))
Step 1
Concept
(25y-2 =(5y)2 ), so it becomes a difference of squares. In exams, treat (5y) as one whole term.
Step 2
Why this answer is correct
The correct answer is A. ((x-5y)(x+5y)). (25y-2 =(5y)2 ), so it becomes a difference of squares. In exams, treat (5y) as one whole term.
Step 3
Exam Tip
(25y-2 =(5y)2 ) है इसलिए वर्गों का अंतर बनेगा। परीक्षा में (5y) को एक पूरा पद मानें।
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\(x^2+12x+35\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(x^2+12x+35\).
#quadratic-factorisation
#sum-product
#school-exam
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? Hint Small clue
A ((x+5)(x+7))
B ((x+1)(x+35))
C ((x+3)(x+9))
D ((x-5)(x-7))
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x+7))
Step 1
Concept
(5+7=12) and \(5\cdot7=35\). In exams, form the middle term from factors of the last term.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x+7)). (5+7=12) and \(5\cdot7=35\). In exams, form the middle term from factors of the last term.
Step 3
Exam Tip
(5+7=12) और \(5\cdot7=35\) है। परीक्षा में अंतिम पद के गुणनखंडों से मध्य पद बनाएं।
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\(x^2-10x+21\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2-10x+21\)?
#quadratic-factorisation
#negative-middle
#school-exam
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? Hint Small clue
A ((x-3)(x-7))
B ((x+3)(x+7))
C ((x-1)(x-21))
D ((x-4)(x-6))
Explanation opens after your attempt
Correct Answer
A. ((x-3)(x-7))
Step 1
Concept
(-3-7=-10) and ((-3)(-7)=21). In exams, when the constant is positive and the middle term is negative, take both factors negative.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)(x-7)). (-3-7=-10) and ((-3)(-7)=21). In exams, when the constant is positive and the middle term is negative, take both factors negative.
Step 3
Exam Tip
(-3-7=-10) और ((-3)(-7)=21) है। परीक्षा में धनात्मक स्थिर पद और ऋणात्मक मध्य पद पर दोनों गुणनखंड ऋणात्मक लें।
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