व्यंजक \(x^2+10x+25\) का गुणनखंड रूप कौन सा है?
What is the factorised form of \(x^2+10x+25\)?
#factorisation
#perfect square
#algebraic identities
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A ((x+5)2 )
B ((x-5)2 )
C ((x+10)(x+25))
D ((x+1)(x+25))
Explanation opens after your attempt
Correct Answer
A. ((x+5)2 )
Step 1
Concept
This is a perfect square trinomial because \(25=5^2\) and \(10x=2\cdot5\cdot x\). Exam tip: identify the perfect square first.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)2 ). This is a perfect square trinomial because \(25=5^2\) and \(10x=2\cdot5\cdot x\). Exam tip: identify the perfect square first.
Step 3
Exam Tip
यह पूर्ण वर्ग त्रिपद है क्योंकि \(25=5^2\) और \(10x=2\cdot5\cdot x\) है। परीक्षा में पहले पूर्ण वर्ग की पहचान करें।
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\(9a^2-25b^2\) को गुणनखंडों में लिखिए।
Write \(9a^2-25b^2\) in factors.
#difference of squares
#factorisation
#identities
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A ((9a-25b)(9a+25b))
B ((3a-5b)(3a+5b))
C ((3a-5b)2 )
D ((9a-5b)(a+25b))
Explanation opens after your attempt
Correct Answer
B. ((3a-5b)(3a+5b))
Step 1
Concept
This is a difference of squares where (9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). Exam tip: take square roots of both terms.
Step 2
Why this answer is correct
The correct answer is B. ((3a-5b)(3a+5b)). This is a difference of squares where (9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). Exam tip: take square roots of both terms.
Step 3
Exam Tip
यह वर्गों का अंतर है जहां (9a-2 =(3a)2 ) और (25b-2 =(5b)2 ) है। परीक्षा में दोनों पदों के वर्गमूल लें।
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\(x^2+7x+12\) के सही गुणनखंड कौन से हैं?
Which are the correct factors of \(x^2+7x+12\)?
#quadratic factorisation
#middle term
#school exam
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A ((x+2)(x+6))
B ((x+3)(x+4))
C ((x-3)(x-4))
D ((x+1)(x+12))
Explanation opens after your attempt
Correct Answer
B. ((x+3)(x+4))
Step 1
Concept
Since (3+4=7) and \(3\cdot4=12\), the correct factors are ((x+3)(x+4)). Exam tip: match both sum and product.
Step 2
Why this answer is correct
The correct answer is B. ((x+3)(x+4)). Since (3+4=7) and \(3\cdot4=12\), the correct factors are ((x+3)(x+4)). Exam tip: match both sum and product.
Step 3
Exam Tip
(3+4=7) और \(3\cdot4=12\) है इसलिए सही गुणनखंड ((x+3)(x+4)) हैं। परीक्षा में योग और गुणनफल दोनों मिलाएं।
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\(4p^2+12pq+9q^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(4p^2+12pq+9q^2\)?
#perfect square trinomial
#factorisation
#class 9
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A ((2p+3q)2 )
B ((4p+9q)2 )
C ((2p-3q)2 )
D ((p+q)(4p+9q))
Explanation opens after your attempt
Correct Answer
A. ((2p+3q)2 )
Step 1
Concept
The first and last terms are perfect squares and the middle term is \(2\cdot2p\cdot3q\). Exam tip: confirm with the (2ab) term.
Step 2
Why this answer is correct
The correct answer is A. ((2p+3q)2 ). The first and last terms are perfect squares and the middle term is \(2\cdot2p\cdot3q\). Exam tip: confirm with the (2ab) term.
Step 3
Exam Tip
पहला और अंतिम पद पूर्ण वर्ग हैं तथा मध्य पद \(2\cdot2p\cdot3q\) है। परीक्षा में (2ab) पद से पुष्टि करें।
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\(y^2-11y+30\) को गुणनखंडित करने पर क्या मिलेगा?
What do we get by factorising \(y^2-11y+30\)?
#quadratic factorisation
#negative middle term
#factors
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A ((y-5)(y-6))
B ((y+5)(y+6))
C ((y-3)(y-10))
D ((y+1)(y-30))
Explanation opens after your attempt
Correct Answer
A. ((y-5)(y-6))
Step 1
Concept
Here (-5-6=-11) and ((-5)(-6)=30). Exam tip: for a negative middle term, both factors may be negative.
Step 2
Why this answer is correct
The correct answer is A. ((y-5)(y-6)). Here (-5-6=-11) and ((-5)(-6)=30). Exam tip: for a negative middle term, both factors may be negative.
Step 3
Exam Tip
(-5-6=-11) और ((-5)(-6)=30) है। परीक्षा में ऋण मध्य पद के लिए दोनों कारक ऋण हो सकते हैं।
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\(16m^2-40mn+25n^2\) का सही गुणनखंड रूप चुनिए।
Choose the correct factorised form of \(16m^2-40mn+25n^2\).
#perfect square
#negative sign
#factorisation
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A ((4m+5n)2 )
B ((4m-5n)2 )
C ((16m-25n)2 )
D ((4m-25n)(4m+n))
Explanation opens after your attempt
Correct Answer
B. ((4m-5n)2 )
Step 1
Concept
The middle term is negative, so the perfect square is ((4m-5n)2 ). Exam tip: check both square roots and sign.
Step 2
Why this answer is correct
The correct answer is B. ((4m-5n)2 ). The middle term is negative, so the perfect square is ((4m-5n)2 ). Exam tip: check both square roots and sign.
Step 3
Exam Tip
मध्य पद ऋण है इसलिए पूर्ण वर्ग ((4m-5n)2 ) बनेगा। परीक्षा में वर्गमूल और चिह्न दोनों जांचें।
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\(a^3-b^3\) का गुणनखंड रूप कौन सा है?
What is the factorised form of \(a^3-b^3\)?
#difference of cubes
#factorisation
#identity
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A ((a-b)\(a^2+ab+b^2\))
B ((a+b)\(a^2-ab+b^2\))
C ((a-b)\(a^2-ab+b^2\))
D ((a-b)3 )
Explanation opens after your attempt
Correct Answer
A. ((a-b)\(a^2+ab+b^2\))
Step 1
Concept
The formula for difference of cubes is (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)). Exam tip: keep all signs positive in the second bracket.
Step 2
Why this answer is correct
The correct answer is A. ((a-b)\(a^2+ab+b^2\)). The formula for difference of cubes is (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)). Exam tip: keep all signs positive in the second bracket.
Step 3
Exam Tip
घनों के अंतर का सूत्र (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)) है। परीक्षा में दूसरे कोष्ठक के सभी चिह्न धन रखें।
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\(a^3+b^3\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(a^3+b^3\)?
#sum of cubes
#factorisation
#algebraic identity
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A ((a-b)\(a^2+ab+b^2\))
B ((a+b)\(a^2-ab+b^2\))
C ((a+b)\(a^2+ab+b^2\))
D ((a+b)3 )
Explanation opens after your attempt
Correct Answer
B. ((a+b)\(a^2-ab+b^2\))
Step 1
Concept
In sum of cubes, the first factor is ((a+b)) and the second is \(a^2-ab+b^2\). Exam tip: remember the negative middle sign.
Step 2
Why this answer is correct
The correct answer is B. ((a+b)\(a^2-ab+b^2\)). In sum of cubes, the first factor is ((a+b)) and the second is \(a^2-ab+b^2\). Exam tip: remember the negative middle sign.
Step 3
Exam Tip
घनों के योग में पहला गुणनखंड ((a+b)) और दूसरा \(a^2-ab+b^2\) होता है। परीक्षा में बीच का चिह्न ऋण याद रखें।
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\(x^2-2x-35\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2-2x-35\)?
#quadratic factorisation
#opposite signs
#expert
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A ((x-7)(x+5))
B ((x+7)(x-5))
C ((x-35)(x+1))
D ((x-7)(x-5))
Explanation opens after your attempt
Correct Answer
A. ((x-7)(x+5))
Step 1
Concept
Since (-7+5=-2) and ((-7)(5)=-35). Exam tip: choose factors with opposite signs carefully.
Step 2
Why this answer is correct
The correct answer is A. ((x-7)(x+5)). Since (-7+5=-2) and ((-7)(5)=-35). Exam tip: choose factors with opposite signs carefully.
Step 3
Exam Tip
(-7+5=-2) और ((-7)(5)=-35) है। परीक्षा में विपरीत चिह्न वाले गुणनखंड सावधानी से चुनें।
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\(6x^2+11x+3\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(6x^2+11x+3\)?
#quadratic factorisation
#splitting middle term
#algebra
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A ((3x+1)(2x+3))
B ((6x+1)(x+3))
C ((3x+3)(2x+1))
D ((x+1)(6x+3))
Explanation opens after your attempt
Correct Answer
A. ((3x+1)(2x+3))
Step 1
Concept
Expanding gives \(6x^2+9x+2x+3=6x^2+11x+3\). Exam tip: verify the split of the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((3x+1)(2x+3)). Expanding gives \(6x^2+9x+2x+3=6x^2+11x+3\). Exam tip: verify the split of the middle term.
Step 3
Exam Tip
विस्तार करने पर \(6x^2+9x+2x+3=6x^2+11x+3\) मिलता है। परीक्षा में मध्य पद विभाजन जांचें।
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\(12a^2-17ab+6b^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(12a^2-17ab+6b^2\)?
#advanced factorisation
#middle term
#splitting
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A ((3a-2b)(4a-3b))
B ((6a-b)(2a-6b))
C ((12a-6b)(a-b))
D ((3a+2b)(4a+3b))
Explanation opens after your attempt
Correct Answer
A. ((3a-2b)(4a-3b))
Step 1
Concept
The terms (-9ab) and (-8ab) combine to (-17ab). Exam tip: use product \(72a^2b^2\) to find the right split.
Step 2
Why this answer is correct
The correct answer is A. ((3a-2b)(4a-3b)). The terms (-9ab) and (-8ab) combine to (-17ab). Exam tip: use product \(72a^2b^2\) to find the right split.
Step 3
Exam Tip
(-9ab) और (-8ab) मिलकर (-17ab) देते हैं। परीक्षा में गुणनफल \(72a^2b^2\) से सही विभाजन खोजें।
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(2xy+6x+5y+15) को समूह बनाकर गुणनखंडित कीजिए।
Factorise (2xy+6x+5y+15) by grouping.
#factorisation by grouping
#common bracket
#algebra
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A ((x+5)(2y+3))
B ((2x+5)(y+3))
C ((2x+3)(y+5))
D ((x+3)(2y+5))
Explanation opens after your attempt
Correct Answer
B. ((2x+5)(y+3))
Step 1
Concept
Grouping gives (2x(y+3)+5(y+3)), so the factor is ((2x+5)(y+3)). Exam tip: look for a common bracket.
Step 2
Why this answer is correct
The correct answer is B. ((2x+5)(y+3)). Grouping gives (2x(y+3)+5(y+3)), so the factor is ((2x+5)(y+3)). Exam tip: look for a common bracket.
Step 3
Exam Tip
समूह (2x(y+3)+5(y+3)) बनता है इसलिए ((2x+5)(y+3)) मिलता है। परीक्षा में समान कोष्ठक खोजें।
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\(a^2+2ab+b^2-c^2\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(a^2+2ab+b^2-c^2\)?
#combined identities
#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)
D ((a+c)(b-c))
Explanation opens after your attempt
Correct Answer
A. ((a+b-c)(a+b+c))
Step 1
Concept
First take (a-2 +2ab+b-2 =(a+b)2 ), then apply difference of squares. Exam tip: apply combined identities stepwise.
Step 2
Why this answer is correct
The correct answer is A. ((a+b-c)(a+b+c)). First take (a-2 +2ab+b-2 =(a+b)2 ), then apply difference of squares. Exam tip: apply combined identities stepwise.
Step 3
Exam Tip
पहले (a-2 +2ab+b-2 =(a+b)2 ) मानें फिर वर्गों का अंतर लगाएं। परीक्षा में मिश्रित पहचानों को क्रम से लागू करें।
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\(25x^2-30xy+9y^2\) को गुणनखंडित कीजिए।
Factorise \(25x^2-30xy+9y^2\).
#perfect square trinomial
#factorisation
#negative middle term
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A ((5x+3y)2 )
B ((25x-9y)2 )
C ((5x-3y)2 )
D ((5x-9y)(5x+y))
Explanation opens after your attempt
Correct Answer
C. ((5x-3y)2 )
Step 1
Concept
It is ((5x)2 -2\cdot5x\cdot3y+(3y)2 ). Exam tip: use the subtraction square for a negative middle term.
Step 2
Why this answer is correct
The correct answer is C. ((5x-3y)2 ). It is ((5x)2 -2\cdot5x\cdot3y+(3y)2 ). Exam tip: use the subtraction square for a negative middle term.
Step 3
Exam Tip
यह ((5x)2 -2\cdot5x\cdot3y+(3y)2 ) है। परीक्षा में ऋण मध्य पद होने पर घटाव वाला वर्ग लें।
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\(x^3+8\) को गुणनखंडित करने पर क्या मिलेगा?
What do we get by factorising \(x^3+8\)?
#sum of cubes
#cubic factorisation
#class 9
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A ((x+2)\(x^2-2x+4\))
B ((x-2)\(x^2+2x+4\))
C ((x+2)\(x^2+2x+4\))
D ((x+2)3 )
Explanation opens after your attempt
Correct Answer
A. ((x+2)\(x^2-2x+4\))
Step 1
Concept
This is \(x^3+2^3\), so use the sum of cubes formula. Exam tip: keep the middle term negative in the second bracket.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)\(x^2-2x+4\)). This is \(x^3+2^3\), so use the sum of cubes formula. Exam tip: keep the middle term negative in the second bracket.
Step 3
Exam Tip
यह \(x^3+2^3\) है इसलिए घनों के योग का सूत्र लगेगा। परीक्षा में दूसरे कोष्ठक में बीच का पद ऋण रखें।
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\(27p^3-q^3\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(27p^3-q^3\).
#difference of cubes
#factorisation
#cubic identity
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A ((3p-q)\(9p^2+3pq+q^2\))
B ((3p+q)\(9p^2-3pq+q^2\))
C ((27p-q)\(p^2+pq+q^2\))
D ((3p-q)3 )
Explanation opens after your attempt
Correct Answer
A. ((3p-q)\(9p^2+3pq+q^2\))
Step 1
Concept
Since (27p-3 =(3p)3 ), it is a difference of cubes. Exam tip: use ((a-b)\(a^2+ab+b^2\)).
Step 2
Why this answer is correct
The correct answer is A. ((3p-q)\(9p^2+3pq+q^2\)). Since (27p-3 =(3p)3 ), it is a difference of cubes. Exam tip: use ((a-b)\(a^2+ab+b^2\)).
Step 3
Exam Tip
(27p-3 =(3p)3 ) है और यह घनों का अंतर है। परीक्षा में ((a-b)\(a^2+ab+b^2\)) लगाएं।
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\(5x^2-20\) का पूर्ण गुणनखंड रूप कौन सा है?
Which is the complete factorised form of \(5x^2-20\)?
#common factor
#difference of squares
#complete factorisation
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A (5\(x^2-4\))
B (5(x-2)(x+2))
C ((5x-20)(x+1))
D (5(x-2)2 )
Explanation opens after your attempt
Correct Answer
B. (5(x-2)(x+2))
Step 1
Concept
First take common factor (5), then factor \(x^2-4\). Exam tip: apply identities after taking the common factor.
Step 2
Why this answer is correct
The correct answer is B. (5(x-2)(x+2)). First take common factor (5), then factor \(x^2-4\). Exam tip: apply identities after taking the common factor.
Step 3
Exam Tip
पहले (5) सामान्य गुणनखंड लें और फिर \(x^2-4\) को तोड़ें। परीक्षा में सामान्य गुणनखंड के बाद पहचान लगाएं।
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\(3a^2b+6ab^2-9ab\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(3a^2b+6ab^2-9ab\)?
#common factor
#algebraic factorisation
#monomials
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A (3ab(a+2b-3))
B (3a(a+2b-3))
C (ab(3a+6b-9ab))
D (3b\(a^2+2b-3\))
Explanation opens after your attempt
Correct Answer
A. (3ab(a+2b-3))
Step 1
Concept
The common factor in all three terms is (3ab). Exam tip: take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (3ab(a+2b-3)). The common factor in all three terms is (3ab). Exam tip: take out the greatest common factor.
Step 3
Exam Tip
तीनों पदों में सामान्य गुणनखंड (3ab) है। परीक्षा में सबसे बड़ा सामान्य गुणनखंड निकालें।
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\(x^2+2xy+y^2-z^2\) का गुणनखंड रूप कौन सा है?
What is the factorised form of \(x^2+2xy+y^2-z^2\)?
#combined factorisation
#perfect square
#difference of squares
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A ((x+y-z)(x+y+z))
B ((x-y-z)(x-y+z))
C ((x+y)2 -z-2 )
D ((x+z)(y-z))
Explanation opens after your attempt
Correct Answer
A. ((x+y-z)(x+y+z))
Step 1
Concept
First (x-2 +2xy+y-2 =(x+y)2 ). Exam tip: use difference of squares after forming the perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((x+y-z)(x+y+z)). First (x-2 +2xy+y-2 =(x+y)2 ). Exam tip: use difference of squares after forming the perfect square.
Step 3
Exam Tip
पहले (x-2 +2xy+y-2 =(x+y)2 ) बनता है। परीक्षा में पूर्ण वर्ग के बाद वर्गों का अंतर लगाएं।
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\(49u^2-v^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(49u^2-v^2\)?
#difference of squares
#factorisation
#identity
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A ((7u-v)(7u+v))
B ((49u-v)(u+v))
C ((7u-v)2 )
D ((7u+v)2 )
Explanation opens after your attempt
Correct Answer
A. ((7u-v)(7u+v))
Step 1
Concept
Since (49u-2 =(7u)2 ), this is a difference of squares. Exam tip: use (\(A^2-B^2\)=(A-B)(A+B)).
Step 2
Why this answer is correct
The correct answer is A. ((7u-v)(7u+v)). Since (49u-2 =(7u)2 ), this is a difference of squares. Exam tip: use (\(A^2-B^2\)=(A-B)(A+B)).
Step 3
Exam Tip
(49u-2 =(7u)2 ) है इसलिए यह वर्गों का अंतर है। परीक्षा में (\(A^2-B^2\)=(A-B)(A+B)) लगाएं।
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\(2x^2+9x+10\) को गुणनखंडित करने पर कौन सा उत्तर सही है?
Which answer is correct after factorising \(2x^2+9x+10\)?
#quadratic factorisation
#verification
#middle term
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A ((2x+5)(x+2))
B ((2x+2)(x+5))
C ((x+5)(x+4))
D ((2x+10)(x+1))
Explanation opens after your attempt
Correct Answer
A. ((2x+5)(x+2))
Step 1
Concept
Expanding gives \(2x^2+4x+5x+10=2x^2+9x+10\). Exam tip: verify the answer by multiplication.
Step 2
Why this answer is correct
The correct answer is A. ((2x+5)(x+2)). Expanding gives \(2x^2+4x+5x+10=2x^2+9x+10\). Exam tip: verify the answer by multiplication.
Step 3
Exam Tip
विस्तार से \(2x^2+4x+5x+10=2x^2+9x+10\) मिलता है। परीक्षा में गुणा करके उत्तर सत्यापित करें।
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\(3x^2-14x+8\) के गुणनखंड कौन से हैं?
What are the factors of \(3x^2-14x+8\)?
#middle term split
#quadratic factorisation
#expert
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A ((3x-2)(x-4))
B ((3x-4)(x-2))
C ((x-8)(3x-1))
D ((3x+2)(x+4))
Explanation opens after your attempt
Correct Answer
A. ((3x-2)(x-4))
Step 1
Concept
The terms (-12x) and (-2x) combine to (-14x). Exam tip: group after splitting the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((3x-2)(x-4)). The terms (-12x) and (-2x) combine to (-14x). Exam tip: group after splitting the middle term.
Step 3
Exam Tip
(-12x) और (-2x) मिलकर (-14x) देते हैं। परीक्षा में मध्य पद विभाजन के बाद समूह बनाएं।
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\(x^2-y^2+2x+2y\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(x^2-y^2+2x+2y\)?
#grouping
#difference of squares
#factorisation
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A ((x+y)(x-y+2))
B ((x-y)(x+y+2))
C ((x+y+2)(x-y))
D ((x+y)(x-y-2))
Explanation opens after your attempt
Correct Answer
A. ((x+y)(x-y+2))
Step 1
Concept
Write it as ((x+y)(x-y)+2(x+y)), then take ((x+y)) common. Exam tip: identify the difference of squares first.
Step 2
Why this answer is correct
The correct answer is A. ((x+y)(x-y+2)). Write it as ((x+y)(x-y)+2(x+y)), then take ((x+y)) common. Exam tip: identify the difference of squares first.
Step 3
Exam Tip
इसे ((x+y)(x-y)+2(x+y)) लिखकर ((x+y)) सामान्य लें। परीक्षा में पहले वर्गों के अंतर को पहचानें।
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(mn+mp+qn+qp) को गुणनखंडों में लिखिए।
Write (mn+mp+qn+qp) in factors.
#factorisation by grouping
#common binomial
#algebra
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A ((m+q)(n+p))
B ((m+n)(p+q))
C ((m+p)(n+q))
D ((mn+q)(p+1))
Explanation opens after your attempt
Correct Answer
A. ((m+q)(n+p))
Step 1
Concept
Grouping gives (m(n+p)+q(n+p)), so the factor is ((m+q)(n+p)). Exam tip: look for the common binomial bracket.
Step 2
Why this answer is correct
The correct answer is A. ((m+q)(n+p)). Grouping gives (m(n+p)+q(n+p)), so the factor is ((m+q)(n+p)). Exam tip: look for the common binomial bracket.
Step 3
Exam Tip
समूह (m(n+p)+q(n+p)) बनता है इसलिए ((m+q)(n+p)) मिलता है। परीक्षा में समान द्विपद कोष्ठक देखें।
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\(8x^3+27y^3\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(8x^3+27y^3\)?
#sum of cubes
#cubic identity
#factorisation
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A ((2x+3y)\(4x^2-6xy+9y^2\))
B ((2x-3y)\(4x^2+6xy+9y^2\))
C ((8x+27y)\(x^2-xy+y^2\))
D ((2x+3y)3 )
Explanation opens after your attempt
Correct Answer
A. ((2x+3y)\(4x^2-6xy+9y^2\))
Step 1
Concept
This is ((2x)3 +(3y)3 ). Exam tip: directly apply the sum of cubes formula.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3y)\(4x^2-6xy+9y^2\)). This is ((2x)3 +(3y)3 ). Exam tip: directly apply the sum of cubes formula.
Step 3
Exam Tip
यह ((2x)3 +(3y)3 ) है। परीक्षा में घनों के योग का सूत्र सीधे लगाएं।
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\(64a^3-125b^3\) का सही गुणनखंड रूप चुनिए।
Choose the correct factorised form of \(64a^3-125b^3\).
#difference of cubes
#cubic factorisation
#identity
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A ((4a-5b)\(16a^2+20ab+25b^2\))
B ((4a+5b)\(16a^2-20ab+25b^2\))
C ((8a-25b)\(8a^2+ab+b^2\))
D ((4a-5b)3 )
Explanation opens after your attempt
Correct Answer
A. ((4a-5b)\(16a^2+20ab+25b^2\))
Step 1
Concept
Here (64a-3 =(4a)3 ) and (125b-3 =(5b)3 ). Exam tip: in the difference formula, the second bracket has positive (20ab).
Step 2
Why this answer is correct
The correct answer is A. ((4a-5b)\(16a^2+20ab+25b^2\)). Here (64a-3 =(4a)3 ) and (125b-3 =(5b)3 ). Exam tip: in the difference formula, the second bracket has positive (20ab).
Step 3
Exam Tip
(64a-3 =(4a)3 ) और (125b-3 =(5b)3 ) हैं। परीक्षा में अंतर के सूत्र में दूसरे कोष्ठक में धन (20ab) आएगा।
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\(x^2+2x-63\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2+2x-63\)?
#quadratic factorisation
#opposite signs
#school exam
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A ((x+9)(x-7))
B ((x-9)(x+7))
C ((x+3)(x-21))
D ((x+63)(x-1))
Explanation opens after your attempt
Correct Answer
A. ((x+9)(x-7))
Step 1
Concept
Since (9-7=2) and (9\cdot(-7)=-63). Exam tip: use opposite signs for a negative constant term.
Step 2
Why this answer is correct
The correct answer is A. ((x+9)(x-7)). Since (9-7=2) and (9\cdot(-7)=-63). Exam tip: use opposite signs for a negative constant term.
Step 3
Exam Tip
(9-7=2) और (9\cdot(-7)=-63) है। परीक्षा में ऋण स्थिर पद के लिए विपरीत चिह्न लें।
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\(7x^2-28xy\) का गुणनखंड रूप क्या है?
What is the factorised form of \(7x^2-28xy\)?
#common factor
#monomial factorisation
#algebra
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A (7x(x-4y))
B (7\(x^2-4y\))
C (x(7x-28))
D (7xy(x-4))
Explanation opens after your attempt
Correct Answer
A. (7x(x-4y))
Step 1
Concept
Both terms have common factor (7x). Exam tip: take out both numerical and variable factors.
Step 2
Why this answer is correct
The correct answer is A. (7x(x-4y)). Both terms have common factor (7x). Exam tip: take out both numerical and variable factors.
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड (7x) है। परीक्षा में चर और संख्यात्मक गुणनखंड दोनों निकालें।
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\(x^2+4xy+4y^2-9z^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+4xy+4y^2-9z^2\).
#combined identity
#perfect square
#difference of squares
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A ((x+2y-3z)(x+2y+3z))
B ((x-2y-3z)(x-2y+3z))
C ((x+2y)2 -3z)
D ((x+3z)(2y-3z))
Explanation opens after your attempt
Correct Answer
A. ((x+2y-3z)(x+2y+3z))
Step 1
Concept
First (x-2 +4xy+4y-2 =(x+2y)2 ), and (9z-2 =(3z)2 ). Exam tip: apply two identities in order.
Step 2
Why this answer is correct
The correct answer is A. ((x+2y-3z)(x+2y+3z)). First (x-2 +4xy+4y-2 =(x+2y)2 ), and (9z-2 =(3z)2 ). Exam tip: apply two identities in order.
Step 3
Exam Tip
पहले (x-2 +4xy+4y-2 =(x+2y)2 ) बनता है और (9z-2 =(3z)2 ) है। परीक्षा में दो पहचानों को क्रम से लगाएं।
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\(a^2-b^2-a+b\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(a^2-b^2-a+b\)?
#grouping
#difference of squares
#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-1)(a+b))
Explanation opens after your attempt
Correct Answer
A. ((a-b)(a+b-1))
Step 1
Concept
Write it as ((a-b)(a+b)-(a-b)), then take ((a-b)) common. Exam tip: also convert the last two terms into a group.
Step 2
Why this answer is correct
The correct answer is A. ((a-b)(a+b-1)). Write it as ((a-b)(a+b)-(a-b)), then take ((a-b)) common. Exam tip: also convert the last two terms into a group.
Step 3
Exam Tip
इसे ((a-b)(a+b)-(a-b)) लिखकर ((a-b)) सामान्य लें। परीक्षा में अंतिम दो पदों को भी समूह में बदलें।
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\(15x^2+22x+8\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(15x^2+22x+8\)?
#quadratic factorisation
#expansion check
#middle term
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A ((3x+2)(5x+4))
B ((15x+2)(x+4))
C ((5x+2)(3x+4))
D ((3x+4)(5x+2))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(5x+4))
Step 1
Concept
((3x+2)(5x+4)) gives \(15x^2+12x+10x+8\). Exam tip: check options by expansion.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(5x+4)). ((3x+2)(5x+4)) gives \(15x^2+12x+10x+8\). Exam tip: check options by expansion.
Step 3
Exam Tip
((3x+2)(5x+4)) से \(15x^2+12x+10x+8\) मिलता है। परीक्षा में विकल्पों को फैलाकर जांचें।
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\(18x^2-21x-10\) को गुणनखंडित कीजिए।
Factorise \(18x^2-21x-10\).
#quadratic factorisation
#negative constant
#expert
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A ((3x-5)(6x+2))
B ((6x-5)(3x+2))
C ((9x+2)(2x-5))
D ((18x+5)(x-2))
Explanation opens after your attempt
Correct Answer
B. ((6x-5)(3x+2))
Step 1
Concept
((6x-5)(3x+2)) gives \(18x^2+12x-15x-10\). Exam tip: confirm that the middle term becomes (-21x).
Step 2
Why this answer is correct
The correct answer is B. ((6x-5)(3x+2)). ((6x-5)(3x+2)) gives \(18x^2+12x-15x-10\). Exam tip: confirm that the middle term becomes (-21x).
Step 3
Exam Tip
((6x-5)(3x+2)) से \(18x^2+12x-15x-10\) मिलता है। परीक्षा में मध्य पद (-21x) बनने की पुष्टि करें।
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\(x^3-6x^2+12x-8\) का गुणनखंड रूप कौन सा है?
What is the factorised form of \(x^3-6x^2+12x-8\)?
#cube identity
#perfect cube
#factorisation
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A ((x-2)3 )
B ((x+2)3 )
C ((x-2)\(x^2+2x+4\))
D ((x-4)\(x^2-2x+2\))
Explanation opens after your attempt
Correct Answer
A. ((x-2)3 )
Step 1
Concept
This is the expansion of ((x-2)3 ). Exam tip: identify the cube identity \(a^3-3a^2b+3ab^2-b^3\).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)3 ). This is the expansion of ((x-2)3 ). Exam tip: identify the cube identity \(a^3-3a^2b+3ab^2-b^3\).
Step 3
Exam Tip
यह ((x-2)3 ) का विस्तार है। परीक्षा में घन पहचान \(a^3-3a^2b+3ab^2-b^3\) पहचानें।
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\(8a^3+12a^2b+6ab^2+b^3\) का गुणनखंड रूप क्या है?
What is the factorised form of \(8a^3+12a^2b+6ab^2+b^3\)?
#perfect cube
#cube identity
#factorisation
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A ((2a+b)3 )
B ((2a-b)3 )
C ((8a+b)3 )
D ((a+2b)3 )
Explanation opens after your attempt
Correct Answer
A. ((2a+b)3 )
Step 1
Concept
It is ((2a)3 +3(2a)2 b+3(2a)b-2 +b-3 ). Exam tip: identify cube coefficients (1), (3), (3), (1).
Step 2
Why this answer is correct
The correct answer is A. ((2a+b)3 ). It is ((2a)3 +3(2a)2 b+3(2a)b-2 +b-3 ). Exam tip: identify cube coefficients (1), (3), (3), (1).
Step 3
Exam Tip
यह ((2a)3 +3(2a)2 b+3(2a)b-2 +b-3 ) है। परीक्षा में घन के गुणांकों (1), (3), (3), (1) को पहचानें।
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\(p^2-q^2+2qr-2pr\) को गुणनखंडित कीजिए।
Factorise \(p^2-q^2+2qr-2pr\).
#grouping
#factorisation
#difference of squares
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A ((p-q)(p+q-2r))
B ((p+q)(p-q+2r))
C ((p-q)(p+q+2r))
D ((p-r)(p+q-2q))
Explanation opens after your attempt
Correct Answer
A. ((p-q)(p+q-2r))
Step 1
Concept
It can be written as ((p-q)(p+q)-2r(p-q)). Exam tip: identify the common bracket ((p-q)).
Step 2
Why this answer is correct
The correct answer is A. ((p-q)(p+q-2r)). It can be written as ((p-q)(p+q)-2r(p-q)). Exam tip: identify the common bracket ((p-q)).
Step 3
Exam Tip
इसे ((p-q)(p+q)-2r(p-q)) लिखा जा सकता है। परीक्षा में समान ((p-q)) कोष्ठक पहचानें।
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\(4x^2+4xy+y^2-16\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(4x^2+4xy+y^2-16\)?
#perfect square
#difference of squares
#factorisation
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A ((2x+y-4)(2x+y+4))
B ((2x-y-4)(2x-y+4))
C ((4x+y-16)(x+y+1))
D ((2x+y)2 -4)
Explanation opens after your attempt
Correct Answer
A. ((2x+y-4)(2x+y+4))
Step 1
Concept
First (4x-2 +4xy+y-2 =(2x+y)2 ), and \(16=4^2\). Exam tip: apply difference of squares at the end.
Step 2
Why this answer is correct
The correct answer is A. ((2x+y-4)(2x+y+4)). First (4x-2 +4xy+y-2 =(2x+y)2 ), and \(16=4^2\). Exam tip: apply difference of squares at the end.
Step 3
Exam Tip
पहले (4x-2 +4xy+y-2 =(2x+y)2 ) और \(16=4^2\) है। परीक्षा में वर्गों का अंतर अंत में लगाएं।
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\(x^2+xy-6y^2\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2+xy-6y^2\)?
#quadratic in two variables
#factorisation
#opposite signs
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A ((x+3y)(x-2y))
B ((x-3y)(x+2y))
C ((x+6y)(x-y))
D ((x-6y)(x+y))
Explanation opens after your attempt
Correct Answer
A. ((x+3y)(x-2y))
Step 1
Concept
Since (3y-2y=y) and (3y\cdot(-2y)=-6y-2 ). Exam tip: think of factors including (y).
Step 2
Why this answer is correct
The correct answer is A. ((x+3y)(x-2y)). Since (3y-2y=y) and (3y\cdot(-2y)=-6y-2 ). Exam tip: think of factors including (y).
Step 3
Exam Tip
(3y-2y=y) और (3y\cdot(-2y)=-6y-2 ) है। परीक्षा में (y) सहित गुणनखंड सोचें।
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\(2a^2+7ab+3b^2\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(2a^2+7ab+3b^2\)?
#two variable quadratic
#factorisation
#middle term
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A ((2a+b)(a+3b))
B ((2a+3b)(a+b))
C ((a+b)(2a+3b))
D ((2a+7b)(a+b))
Explanation opens after your attempt
Correct Answer
A. ((2a+b)(a+3b))
Step 1
Concept
((2a+b)(a+3b)) gives \(2a^2+6ab+ab+3b^2\). Exam tip: make the middle term (7ab).
Step 2
Why this answer is correct
The correct answer is A. ((2a+b)(a+3b)). ((2a+b)(a+3b)) gives \(2a^2+6ab+ab+3b^2\). Exam tip: make the middle term (7ab).
Step 3
Exam Tip
((2a+b)(a+3b)) से \(2a^2+6ab+ab+3b^2\) मिलता है। परीक्षा में मध्य पद (7ab) बनने दें।
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\(5m^2-13mn-6n^2\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(5m^2-13mn-6n^2\)?
#quadratic factorisation
#two variables
#opposite signs
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A ((5m+2n)(m-3n))
B ((5m-2n)(m+3n))
C ((m-6n)(5m+n))
D ((5m-6n)(m+n))
Explanation opens after your attempt
Correct Answer
A. ((5m+2n)(m-3n))
Step 1
Concept
((5m+2n)(m-3n)) gives \(5m^2-15mn+2mn-6n^2\). Exam tip: use opposite signs for a negative constant term.
Step 2
Why this answer is correct
The correct answer is A. ((5m+2n)(m-3n)). ((5m+2n)(m-3n)) gives \(5m^2-15mn+2mn-6n^2\). Exam tip: use opposite signs for a negative constant term.
Step 3
Exam Tip
((5m+2n)(m-3n)) से \(5m^2-15mn+2mn-6n^2\) मिलता है। परीक्षा में ऋण स्थिर पद के लिए विपरीत चिह्न रखें।
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\(x^2+6x+9-y^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+6x+9-y^2\)?
#combined identity
#perfect square
#difference of squares
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A ((x+3-y)(x+3+y))
B ((x-3-y)(x-3+y))
C ((x+3)2 -y)
D ((x+y+3)(x-y-3))
Explanation opens after your attempt
Correct Answer
A. ((x+3-y)(x+3+y))
Step 1
Concept
Here (x-2 +6x+9=(x+3)2 ), then difference of squares applies. Exam tip: first convert the trinomial into a perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((x+3-y)(x+3+y)). Here (x-2 +6x+9=(x+3)2 ), then difference of squares applies. Exam tip: first convert the trinomial into a perfect square.
Step 3
Exam Tip
(x-2 +6x+9=(x+3)2 ) है और फिर वर्गों का अंतर लगता है। परीक्षा में पहले त्रिपद को पूर्ण वर्ग बनाएं।
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\(81r^2-18rs+s^2\) को गुणनखंडित कीजिए।
Factorise \(81r^2-18rs+s^2\).
#perfect square trinomial
#negative middle term
#factorisation
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A ((9r-s)2 )
B ((9r+s)2 )
C ((81r-s)2 )
D ((9r-s)(9r+s))
Explanation opens after your attempt
Correct Answer
A. ((9r-s)2 )
Step 1
Concept
It is ((9r)2 -2\cdot9r\cdot s+s-2 ). Exam tip: choose the answer by the sign of the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((9r-s)2 ). It is ((9r)2 -2\cdot9r\cdot s+s-2 ). Exam tip: choose the answer by the sign of the middle term.
Step 3
Exam Tip
यह ((9r)2 -2\cdot9r\cdot s+s-2 ) है। परीक्षा में मध्य पद के चिह्न से उत्तर चुनें।
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\(a^2+ab+ac+bc\) को गुणनखंडों में लिखिए।
Write \(a^2+ab+ac+bc\) in factors.
#grouping
#common bracket
#factorisation
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A ((a+b)(a+c))
B ((a+c)(a-b))
C ((a+b)(a-c))
D ((a+bc)(a+1))
Explanation opens after your attempt
Correct Answer
A. ((a+b)(a+c))
Step 1
Concept
Grouping gives (a(a+b)+c(a+b)), so the factor is ((a+b)(a+c)). Exam tip: learn grouping in four-term expressions.
Step 2
Why this answer is correct
The correct answer is A. ((a+b)(a+c)). Grouping gives (a(a+b)+c(a+b)), so the factor is ((a+b)(a+c)). Exam tip: learn grouping in four-term expressions.
Step 3
Exam Tip
समूह (a(a+b)+c(a+b)) बनता है इसलिए ((a+b)(a+c)) मिलता है। परीक्षा में चार पदों में समूह बनाना सीखें।
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\(36x^2-49y^2\) का गुणनखंड रूप कौन सा है?
What is the factorised form of \(36x^2-49y^2\)?
#difference of squares
#factorisation
#identity
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A ((6x-7y)(6x+7y))
B ((36x-49y)(x+y))
C ((6x-7y)2 )
D ((18x-7y)(2x+7y))
Explanation opens after your attempt
Correct Answer
A. ((6x-7y)(6x+7y))
Step 1
Concept
Here (36x-2 =(6x)2 ) and (49y-2 =(7y)2 ). Exam tip: quickly recognize the difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((6x-7y)(6x+7y)). Here (36x-2 =(6x)2 ) and (49y-2 =(7y)2 ). Exam tip: quickly recognize the difference of squares.
Step 3
Exam Tip
(36x-2 =(6x)2 ) और (49y-2 =(7y)2 ) हैं। परीक्षा में वर्गों का अंतर तुरंत पहचानें।
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\(x^2-16x+64\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(x^2-16x+64\)?
#perfect square trinomial
#factorisation
#negative middle term
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A ((x-8)2 )
B ((x+8)2 )
C ((x-4)2 )
D ((x-16)(x+4))
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 )
Step 1
Concept
Since \(64=8^2\) and \(-16x=-2\cdot8\cdot x\). Exam tip: identify perfect square trinomials with signs.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 ). Since \(64=8^2\) and \(-16x=-2\cdot8\cdot x\). Exam tip: identify perfect square trinomials with signs.
Step 3
Exam Tip
\(64=8^2\) और \(-16x=-2\cdot8\cdot x\) है। परीक्षा में पूर्ण वर्ग त्रिपद को चिह्न सहित पहचानें।
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\(10x^2+31x+24\) के गुणनखंड कौन से हैं?
What are the factors of \(10x^2+31x+24\)?
#quadratic factorisation
#middle term
#expert
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A ((2x+3)(5x+8))
B ((10x+3)(x+8))
C ((5x+3)(2x+8))
D ((2x+8)(5x+3))
Explanation opens after your attempt
Correct Answer
A. ((2x+3)(5x+8))
Step 1
Concept
((2x+3)(5x+8)) gives \(10x^2+16x+15x+24\). Exam tip: add both parts of the middle term.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)(5x+8)). ((2x+3)(5x+8)) gives \(10x^2+16x+15x+24\). Exam tip: add both parts of the middle term.
Step 3
Exam Tip
((2x+3)(5x+8)) से \(10x^2+16x+15x+24\) मिलता है। परीक्षा में मध्य पद के दोनों हिस्से जोड़कर देखें।
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\(14x^2-23x+6\) का सही गुणनखंड रूप चुनिए।
Choose the correct factorised form of \(14x^2-23x+6\).
#quadratic factorisation
#negative middle term
#verification
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A ((7x-3)(2x-2))
B ((7x-2)(2x-3))
C ((14x-3)(x-2))
D ((2x-7)(7x-6))
Explanation opens after your attempt
Correct Answer
B. ((7x-2)(2x-3))
Step 1
Concept
((7x-2)(2x-3)) gives \(14x^2-21x-4x+6\). Exam tip: check that the middle term becomes (-23x), not (-25x).
Step 2
Why this answer is correct
The correct answer is B. ((7x-2)(2x-3)). ((7x-2)(2x-3)) gives \(14x^2-21x-4x+6\). Exam tip: check that the middle term becomes (-23x), not (-25x).
Step 3
Exam Tip
((7x-2)(2x-3)) से \(14x^2-21x-4x+6\) मिलता है। परीक्षा में (-25x) नहीं बल्कि (-23x) बनने की जांच करें।
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\(x^3+y^3+x^2y+xy^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^3+y^3+x^2y+xy^2\)?
#grouping
#cubic factorisation
#common binomial
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A ((x+y)\(x^2+y^2\))
B ((x+y)\(x^2+xy+y^2\))
C ((x+y)3 )
D ((x-y)\(x^2+xy+y^2\))
Explanation opens after your attempt
Correct Answer
B. ((x+y)\(x^2+xy+y^2\))
Step 1
Concept
Grouping all terms gives a common factor like (x-2 (x+y)+y-2 (x+y)+xy(x+y)). Exam tip: take ((x+y)) common and add the remaining terms.
Step 2
Why this answer is correct
The correct answer is B. ((x+y)\(x^2+xy+y^2\)). Grouping all terms gives a common factor like (x-2 (x+y)+y-2 (x+y)+xy(x+y)). Exam tip: take ((x+y)) common and add the remaining terms.
Step 3
Exam Tip
सभी पदों को समूहित करने पर (x-2 (x+y)+y-2 (x+y)+xy(x+y)) जैसा समान गुणनखंड बनता है। परीक्षा में ((x+y)) सामान्य लेकर शेष पद जोड़ें।
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\(a^2+4b^2+c^2+4ab+2ac+4bc\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(a^2+4b^2+c^2+4ab+2ac+4bc\)?
#trinomial square
#factorisation
#algebraic identity
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A ((a+2b+c)2 )
B ((a+2b-c)2 )
C ((a+b+c)2 )
D ((a+4b+c)2 )
Explanation opens after your attempt
Correct Answer
A. ((a+2b+c)2 )
Step 1
Concept
This is a trinomial square with terms (a), (2b), and (c). Exam tip: confirm using pair terms (4ab), (2ac), and (4bc).
Step 2
Why this answer is correct
The correct answer is A. ((a+2b+c)2 ). This is a trinomial square with terms (a), (2b), and (c). Exam tip: confirm using pair terms (4ab), (2ac), and (4bc).
Step 3
Exam Tip
यह तीन पदों के वर्ग का रूप है जहां पद (a), (2b), (c) हैं। परीक्षा में जोड़ीदार पद (4ab), (2ac), (4bc) से पुष्टि करें।
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\(4x^2-12xy+9y^2-25\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(4x^2-12xy+9y^2-25\)?
#combined identity
#perfect square
#difference of squares
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A ((2x-3y-5)(2x-3y+5))
B ((2x+3y-5)(2x+3y+5))
C ((4x-9y-25)(x+y+1))
D ((2x-3y)2 -5)
Explanation opens after your attempt
Correct Answer
A. ((2x-3y-5)(2x-3y+5))
Step 1
Concept
First (4x-2 -12xy+9y-2 =(2x-3y)2 ), then use difference of squares with \(25=5^2\). Exam tip: form the perfect square and factor further.
Step 2
Why this answer is correct
The correct answer is A. ((2x-3y-5)(2x-3y+5)). First (4x-2 -12xy+9y-2 =(2x-3y)2 ), then use difference of squares with \(25=5^2\). Exam tip: form the perfect square and factor further.
Step 3
Exam Tip
पहले (4x-2 -12xy+9y-2 =(2x-3y)2 ) बनता है फिर \(25=5^2\) से वर्गों का अंतर लगाएं। परीक्षा में पूर्ण वर्ग बनाकर अगला गुणनखंड करें।
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\(x^2+5xy+6y^2-4x-12y\) को गुणनखंडित करने पर सही रूप क्या है?
What is the correct factorised form of \(x^2+5xy+6y^2-4x-12y\)?
#factorisation by grouping
#two variable quadratic
#common bracket
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A ((x+2y)(x+3y-4))
B ((x+3y)(x+2y-4))
C ((x-2y)(x-3y+4))
D ((x+6y)(x-y-4))
Explanation opens after your attempt
Correct Answer
A. ((x+2y)(x+3y-4))
Step 1
Concept
Grouping gives (x(x+3y-4)+2y(x+3y-4)). Exam tip: first make groups that produce a common bracket.
Step 2
Why this answer is correct
The correct answer is A. ((x+2y)(x+3y-4)). Grouping gives (x(x+3y-4)+2y(x+3y-4)). Exam tip: first make groups that produce a common bracket.
Step 3
Exam Tip
समूह बनाने पर (x(x+3y-4)+2y(x+3y-4)) मिलता है। परीक्षा में पहले ऐसे समूह बनाएं जिनमें समान कोष्ठक आए।
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