\(6x^2+17x+12\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(6x^2+17x+12\)?
#factorisation
#quadratic
#splitting middle term
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A ((2x+3)(3x+4))
B ((6x+3)(x+4))
C ((2x+4)(3x+3))
D ((x+3)(6x+4))
Explanation opens after your attempt
Correct Answer
A. ((2x+3)(3x+4))
Step 1
Concept
On multiplying we get \(6x^2+8x+9x+12=6x^2+17x+12\). Exam tip: check by adding the middle terms.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3)(3x+4)). On multiplying we get \(6x^2+8x+9x+12=6x^2+17x+12\). Exam tip: check by adding the middle terms.
Step 3
Exam Tip
गुणा करने पर \(6x^2+8x+9x+12=6x^2+17x+12\) मिलता है। परीक्षा में बीच के पदों को जोड़कर जांचें।
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\(12a^2-7a-10\) के गुणनखंड कौन से हैं?
What are the factors of \(12a^2-7a-10\)?
#quadratic factorisation
#hard algebra
#signs
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A ((3a+2)(4a-5))
B ((3a-5)(4a+2))
C ((2a-5)(6a+2))
D ((4a-5)(3a+2))
Explanation opens after your attempt
Correct Answer
D. ((4a-5)(3a+2))
Step 1
Concept
Expanding ((4a-5)(3a+2)) gives \(12a^2+8a-15a-10\). Exam tip: add opposite-signed terms carefully.
Step 2
Why this answer is correct
The correct answer is D. ((4a-5)(3a+2)). Expanding ((4a-5)(3a+2)) gives \(12a^2+8a-15a-10\). Exam tip: add opposite-signed terms carefully.
Step 3
Exam Tip
((4a-5)(3a+2)) फैलाने पर \(12a^2+8a-15a-10\) मिलता है। परीक्षा में विपरीत चिन्हों वाले पदों का योग ध्यान से करें।
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\(9p^2-30pq+25q^2\) को गुणनखंडित करने पर क्या मिलेगा?
What is obtained by factorising \(9p^2-30pq+25q^2\)?
#perfect square
#factorisation
#two variables
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A ((3p-5q)2 )
B ((3p+5q)2 )
C ((9p-25q)2 )
D ((3p-25q)(3p-q))
Explanation opens after your attempt
Correct Answer
A. ((3p-5q)2 )
Step 1
Concept
It is of the form ((3p)2 -2(3p)(5q)+(5q)2 ). Exam tip: identify the perfect square trinomial.
Step 2
Why this answer is correct
The correct answer is A. ((3p-5q)2 ). It is of the form ((3p)2 -2(3p)(5q)+(5q)2 ). Exam tip: identify the perfect square trinomial.
Step 3
Exam Tip
यह ((3p)2 -2(3p)(5q)+(5q)2 ) का रूप है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।
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\(25x^2-64y^2\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(25x^2-64y^2\)?
#difference of squares
#factorisation
#identity
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A ((25x-64y)(25x+64y))
B ((5x-8y)(5x+8y))
C ((5x-64y)(5x+y))
D ((25x-8y)(x+8y))
Explanation opens after your attempt
Correct Answer
B. ((5x-8y)(5x+8y))
Step 1
Concept
Here (25x-2 =(5x)2 ) and (64y-2 =(8y)2 ). Exam tip: take square roots of both squares.
Step 2
Why this answer is correct
The correct answer is B. ((5x-8y)(5x+8y)). Here (25x-2 =(5x)2 ) and (64y-2 =(8y)2 ). Exam tip: take square roots of both squares.
Step 3
Exam Tip
(25x-2 =(5x)2 ) और (64y-2 =(8y)2 ) है। परीक्षा में दोनों वर्गों की वर्गमूल निकालें।
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\(4m^2+12mn+9n^2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(4m^2+12mn+9n^2\)?
#perfect square
#binomial square
#factorisation
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A ((2m-3n)2 )
B ((4m+9n)2 )
C ((2m+3n)2 )
D ((m+3n)(4m+3n))
Explanation opens after your attempt
Correct Answer
C. ((2m+3n)2 )
Step 1
Concept
Here (4m-2 =(2m)2 ), (9n-2 =(3n)2 ), and the middle term is (2(2m)(3n)). Exam tip: match all three terms.
Step 2
Why this answer is correct
The correct answer is C. ((2m+3n)2 ). Here (4m-2 =(2m)2 ), (9n-2 =(3n)2 ), and the middle term is (2(2m)(3n)). Exam tip: match all three terms.
Step 3
Exam Tip
(4m-2 =(2m)2 ), (9n-2 =(3n)2 ) और बीच का पद (2(2m)(3n)) है। परीक्षा में तीनों पदों को मिलाएं।
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\(x^2-13x+42\) को किस रूप में लिखा जाएगा?
In which form will \(x^2-13x+42\) be written?
#trinomial factorisation
#signs
#quadratic
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A ((x-6)(x-7))
B ((x+6)(x+7))
C ((x-3)(x-14))
D ((x+3)(x-14))
Explanation opens after your attempt
Correct Answer
A. ((x-6)(x-7))
Step 1
Concept
Since (-6-7=-13) and ((-6)(-7)=42). Exam tip: use two negative signs for positive last term and negative middle term.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)(x-7)). Since (-6-7=-13) and ((-6)(-7)=42). Exam tip: use two negative signs for positive last term and negative middle term.
Step 3
Exam Tip
(-6-7=-13) और ((-6)(-7)=42) है। परीक्षा में धनात्मक अंतिम पद और ऋणात्मक मध्य पद के लिए दोनों चिन्ह ऋणात्मक लें।
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\(2x^2-11x+12\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(2x^2-11x+12\)?
#splitting middle term
#factorisation
#quadratic
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A ((2x-3)(x-4))
B ((2x-3)(x+4))
C ((2x-8)(x-3))
D ((x-3)(2x-4))
Explanation opens after your attempt
Correct Answer
A. ((2x-3)(x-4))
Step 1
Concept
((2x-3)(x-4)) gives \(2x^2-8x-3x+12\). Exam tip: confirm the middle term (-11x).
Step 2
Why this answer is correct
The correct answer is A. ((2x-3)(x-4)). ((2x-3)(x-4)) gives \(2x^2-8x-3x+12\). Exam tip: confirm the middle term (-11x).
Step 3
Exam Tip
((2x-3)(x-4)) से \(2x^2-8x-3x+12\) मिलता है। परीक्षा में मध्य पद (-11x) की पुष्टि करें।
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\(16a^2-40ab+25b^2\) किसका पूर्ण वर्ग है?
Whose perfect square is \(16a^2-40ab+25b^2\)?
#perfect square
#minus identity
#factorisation
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A ((4a-5b)2 )
B ((4a+5b)2 )
C ((16a-25b)2 )
D ((8a-5b)2 )
Explanation opens after your attempt
Correct Answer
A. ((4a-5b)2 )
Step 1
Concept
Here (16a-2 =(4a)2 ) and (25b-2 =(5b)2 ), with middle term (-2(4a)(5b)). Exam tip: identify negative perfect squares.
Step 2
Why this answer is correct
The correct answer is A. ((4a-5b)2 ). Here (16a-2 =(4a)2 ) and (25b-2 =(5b)2 ), with middle term (-2(4a)(5b)). Exam tip: identify negative perfect squares.
Step 3
Exam Tip
(16a-2 =(4a)2 ) और (25b-2 =(5b)2 ), बीच का पद (-2(4a)(5b)) है। परीक्षा में ऋणात्मक पूर्ण वर्ग पहचानें।
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\(8x^2+2x-3\) का गुणनखंड रूप क्या है?
What is the factorised form of \(8x^2+2x-3\)?
#factorisation
#quadratic
#signs
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A ((4x+3)(2x-1))
B ((4x-3)(2x+1))
C ((8x-3)(x+1))
D ((2x-3)(4x+1))
Explanation opens after your attempt
Correct Answer
A. ((4x+3)(2x-1))
Step 1
Concept
((4x+3)(2x-1)) gives \(8x^2-4x+6x-3\). Exam tip: add opposite-signed terms correctly.
Step 2
Why this answer is correct
The correct answer is A. ((4x+3)(2x-1)). ((4x+3)(2x-1)) gives \(8x^2-4x+6x-3\). Exam tip: add opposite-signed terms correctly.
Step 3
Exam Tip
((4x+3)(2x-1)) से \(8x^2-4x+6x-3\) मिलता है। परीक्षा में विपरीत चिन्हों के पदों को सही जोड़ें।
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\(49u^2-v^2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(49u^2-v^2\)?
#difference of squares
#two variables
#factorisation
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A ((49u-v)(49u+v))
B ((7u-v)(7u+v))
C ((7u-v)2 )
D ((u-v)(49u+v))
Explanation opens after your attempt
Correct Answer
B. ((7u-v)(7u+v))
Step 1
Concept
(49u-2 =(7u)2 ), and \(v^2\) is the second square. Exam tip: apply the difference of squares form.
Step 2
Why this answer is correct
The correct answer is B. ((7u-v)(7u+v)). (49u-2 =(7u)2 ), and \(v^2\) is the second square. Exam tip: apply the difference of squares form.
Step 3
Exam Tip
(49u-2 =(7u)2 ) है और \(v^2\) दूसरा वर्ग है। परीक्षा में अंतर के वर्गों का रूप लगाएं।
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\(3y^2+14y+8\) को गुणनखंडित कीजिए।
Factorise \(3y^2+14y+8\).
#quadratic factorisation
#checking
#algebra
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A ((3y+2)(y+4))
B ((3y+4)(y+2))
C ((y+2)(3y+8))
D ((3y+8)(y+1))
Explanation opens after your attempt
Correct Answer
B. ((3y+4)(y+2))
Step 1
Concept
((3y+2)(y+4)) gives (12y+2y), while ((3y+4)(y+2)) is correct. Exam tip: verify by expansion.
Step 2
Why this answer is correct
The correct answer is B. ((3y+4)(y+2)). ((3y+2)(y+4)) gives (12y+2y), while ((3y+4)(y+2)) is correct. Exam tip: verify by expansion.
Step 3
Exam Tip
((3y+2)(y+4)) से (14y) नहीं बल्कि (12y+2y) मिलता है, जबकि ((3y+4)(y+2)) सही है। परीक्षा में फैलाकर जांचें।
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\(27p^3-8q^3\) के लिए सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form for \(27p^3-8q^3\)?
#cube identity
#factorisation
#algebraic identities
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A ((3p-2q)\(9p^2+6pq+4q^2\))
B ((3p+2q)\(9p^2-6pq+4q^2\))
C ((27p-8q)\(p^2+pq+q^2\))
D ((3p-2q)\(9p^2-6pq+4q^2\))
Explanation opens after your attempt
Correct Answer
A. ((3p-2q)\(9p^2+6pq+4q^2\))
Step 1
Concept
This is ((3p)3 -(2q)3 ), and (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)). Exam tip: identify cube roots first.
Step 2
Why this answer is correct
The correct answer is A. ((3p-2q)\(9p^2+6pq+4q^2\)). This is ((3p)3 -(2q)3 ), and (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)). Exam tip: identify cube roots first.
Step 3
Exam Tip
यह ((3p)3 -(2q)3 ) है और (a-3 -b-3 =(a-b)\(a^2+ab+b^2\)) लगता है। परीक्षा में घन मूल पहले पहचानें।
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\(x^3+64\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^3+64\)?
#sum of cubes
#factorisation
#identity
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A ((x+4)\(x^2-4x+16\))
B ((x-4)\(x^2+4x+16\))
C ((x+4)\(x^2+4x+16\))
D ((x+8)\(x^2-8x+64\))
Explanation opens after your attempt
Correct Answer
A. ((x+4)\(x^2-4x+16\))
Step 1
Concept
Since \(64=4^3\), use the \(a^3+b^3\) formula. Exam tip: keep the middle sign negative in sum of cubes.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)\(x^2-4x+16\)). Since \(64=4^3\), use the \(a^3+b^3\) formula. Exam tip: keep the middle sign negative in sum of cubes.
Step 3
Exam Tip
\(64=4^3\), इसलिए \(x^3+64\) में \(a^3+b^3\) का सूत्र लगेगा। परीक्षा में योग के घन में बीच का चिन्ह ऋणात्मक रखें।
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\(5x^2y-15xy^2+10xy\) का सबसे सरल गुणनखंड रूप क्या है?
What is the simplest factorised form of \(5x^2y-15xy^2+10xy\)?
#common factor
#three terms
#factorisation
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A (5xy(x-3y+2))
B (5x\(xy-3y^2+2y\))
C (xy(5x-15y+10))
D (10xy(x-3y+2))
Explanation opens after your attempt
Correct Answer
A. (5xy(x-3y+2))
Step 1
Concept
The greatest common factor of all three terms is (5xy). Exam tip: keep the inside expression simplified.
Step 2
Why this answer is correct
The correct answer is A. (5xy(x-3y+2)). The greatest common factor of all three terms is (5xy). Exam tip: keep the inside expression simplified.
Step 3
Exam Tip
तीनों पदों में सबसे बड़ा सामान्य गुणनखंड (5xy) है। परीक्षा में अंदर का रूप सरल रखें।
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\(x^4-81\) को पहले किस पहचान से तोड़ना सबसे उचित है?
Which identity is most suitable first for factorising \(x^4-81\)?
#difference of squares
#higher powers
#factorisation
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A दो वर्गों का अंतर / Difference of two squares
B पूर्ण वर्ग त्रिपद / Perfect square trinomial
C सामान्य गुणनखंड / Common factor
D घनों का योग / Sum of cubes
Explanation opens after your attempt
Correct Answer
A. दो वर्गों का अंतर / Difference of two squares
Step 1
Concept
(x-4 -81=\(x^2\)2 -92 ). Exam tip: view higher powers as squares when possible.
Step 2
Why this answer is correct
The correct answer is A. दो वर्गों का अंतर / Difference of two squares. (x-4 -81=\(x^2\)2 -92 ). Exam tip: view higher powers as squares when possible.
Step 3
Exam Tip
(x-4 -81=\(x^2\)2 -92 ) है। परीक्षा में बड़ी घात को भी वर्ग के रूप में देखें।
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\(x^4-81\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(x^4-81\)?
#complete factorisation
#difference of squares
#higher powers
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A (\(x^2-9\)\(x^2+9\))
B ((x-3)(x+3)\(x^2+9\))
C ((x-9)(x+9))
D ((x-3)2 (x+3)2 )
Explanation opens after your attempt
Correct Answer
B. ((x-3)(x+3)\(x^2+9\))
Step 1
Concept
First (x-4 -81=\(x^2-9\)\(x^2+9\)), then (x-2 -9=(x-3)(x+3)). Exam tip: factor further when possible.
Step 2
Why this answer is correct
The correct answer is B. ((x-3)(x+3)\(x^2+9\)). First (x-4 -81=\(x^2-9\)\(x^2+9\)), then (x-2 -9=(x-3)(x+3)). Exam tip: factor further when possible.
Step 3
Exam Tip
पहले (x-4 -81=\(x^2-9\)\(x^2+9\)), फिर (x-2 -9=(x-3)(x+3)) होता है। परीक्षा में आगे टूट सकने वाले भाग को फिर तोड़ें।
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(6ab+9a+10b+15) को समूह बनाकर गुणनखंडित करें।
Factorise (6ab+9a+10b+15) by grouping.
#factorisation by grouping
#common binomial
#algebra
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+10 Time+ 10 sec extra
? Hint Small clue
A ((3a+5)(2b+3))
B ((2b+3)(3a+5))
C ((3a+10)(2b+9))
D ((6a+10)(b+15))
Explanation opens after your attempt
Correct Answer
B. ((2b+3)(3a+5))
Step 1
Concept
Grouping gives (3a(2b+3)+5(2b+3)). Exam tip: take out the common binomial.
Step 2
Why this answer is correct
The correct answer is B. ((2b+3)(3a+5)). Grouping gives (3a(2b+3)+5(2b+3)). Exam tip: take out the common binomial.
Step 3
Exam Tip
समूह करने पर (3a(2b+3)+5(2b+3)) मिलता है। परीक्षा में समान द्विपद को बाहर निकालें।
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\(x^2+xy-6y^2\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(x^2+xy-6y^2\)?
#trinomial
#two variables
#factorisation
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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
The sum of (3y) and (-2y) is (y), and the product is \(-6y^2\). Exam tip: watch the signs of (y)-terms.
Step 2
Why this answer is correct
The correct answer is A. ((x+3y)(x-2y)). The sum of (3y) and (-2y) is (y), and the product is \(-6y^2\). Exam tip: watch the signs of (y)-terms.
Step 3
Exam Tip
(3y) और (-2y) का योग (y) और गुणनफल \(-6y^2\) है। परीक्षा में (y) वाले पदों के चिन्ह देखें।
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\(2x^2+7xy+3y^2\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(2x^2+7xy+3y^2\)?
#two variable quadratic
#factorisation
#middle term
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A ((2x+y)(x+3y))
B ((2x+3y)(x+y))
C ((x+y)(2x+3y))
D ((2x-y)(x-3y))
Explanation opens after your attempt
Correct Answer
B. ((2x+3y)(x+y))
Step 1
Concept
((2x+3y)(x+y)) gives \(2x^2+2xy+3xy+3y^2\). Exam tip: check the sum of (xy)-terms.
Step 2
Why this answer is correct
The correct answer is B. ((2x+3y)(x+y)). ((2x+3y)(x+y)) gives \(2x^2+2xy+3xy+3y^2\). Exam tip: check the sum of (xy)-terms.
Step 3
Exam Tip
((2x+3y)(x+y)) से \(2x^2+2xy+3xy+3y^2\) मिलता है। परीक्षा में (xy) पदों का योग जांचें।
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\(12x^2-23xy+10y^2\) के गुणनखंड कौन से हैं?
What are the factors of \(12x^2-23xy+10y^2\)?
#two variables
#hard factorisation
#signs
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A ((3x-2y)(4x-5y))
B ((3x-5y)(4x-2y))
C ((6x-5y)(2x-2y))
D ((12x-10y)(x-y))
Explanation opens after your attempt
Correct Answer
A. ((3x-2y)(4x-5y))
Step 1
Concept
((3x-2y)(4x-5y)) gives \(12x^2-15xy-8xy+10y^2\). Exam tip: add both negative middle terms.
Step 2
Why this answer is correct
The correct answer is A. ((3x-2y)(4x-5y)). ((3x-2y)(4x-5y)) gives \(12x^2-15xy-8xy+10y^2\). Exam tip: add both negative middle terms.
Step 3
Exam Tip
((3x-2y)(4x-5y)) से \(12x^2-15xy-8xy+10y^2\) मिलता है। परीक्षा में दोनों ऋणात्मक मध्य पद जोड़ें।
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\(a^3+b^3\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(a^3+b^3\)?
#sum of cubes
#identity
#factorisation
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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)\(a^2-ab+b^2\))
Explanation opens after your attempt
Correct Answer
A. ((a+b)\(a^2-ab+b^2\))
Step 1
Concept
For sum of cubes, the first factor is (a+b) and the second is \(a^2-ab+b^2\). Exam tip: remember the order of signs.
Step 2
Why this answer is correct
The correct answer is A. ((a+b)\(a^2-ab+b^2\)). For sum of cubes, the first factor is (a+b) and the second is \(a^2-ab+b^2\). Exam tip: remember the order of signs.
Step 3
Exam Tip
घनों के योग में पहला गुणनखंड (a+b) और दूसरा \(a^2-ab+b^2\) होता है। परीक्षा में चिन्हों का क्रम याद रखें।
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\(a^3-b^3\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(a^3-b^3\)?
#difference of cubes
#identity
#factorisation
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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)\(a^2+ab+b^2\))
Explanation opens after your attempt
Correct Answer
B. ((a-b)\(a^2+ab+b^2\))
Step 1
Concept
For difference of cubes, the first factor is (a-b) and the second is \(a^2+ab+b^2\). Exam tip: keep sum and difference formulas separate.
Step 2
Why this answer is correct
The correct answer is B. ((a-b)\(a^2+ab+b^2\)). For difference of cubes, the first factor is (a-b) and the second is \(a^2+ab+b^2\). Exam tip: keep sum and difference formulas separate.
Step 3
Exam Tip
घनों के अंतर में पहला गुणनखंड (a-b) और दूसरा \(a^2+ab+b^2\) होता है। परीक्षा में अंतर और योग के सूत्र अलग रखें।
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\(8m^3+27n^3\) को गुणनखंडित कीजिए।
Factorise \(8m^3+27n^3\).
#sum of cubes
#two variables
#factorisation
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A ((2m+3n)\(4m^2-6mn+9n^2\))
B ((2m-3n)\(4m^2+6mn+9n^2\))
C ((8m+27n)\(m^2-mn+n^2\))
D ((2m+3n)\(4m^2+6mn+9n^2\))
Explanation opens after your attempt
Correct Answer
A. ((2m+3n)\(4m^2-6mn+9n^2\))
Step 1
Concept
This is ((2m)3 +(3n)3 ). Exam tip: in \(a^3+b^3\), the middle term of the second bracket is negative.
Step 2
Why this answer is correct
The correct answer is A. ((2m+3n)\(4m^2-6mn+9n^2\)). This is ((2m)3 +(3n)3 ). Exam tip: in \(a^3+b^3\), the middle term of the second bracket is negative.
Step 3
Exam Tip
यह ((2m)3 +(3n)3 ) है। परीक्षा में \(a^3+b^3\) में दूसरे कोष्ठक का बीच वाला पद ऋणात्मक होता है।
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\(125x^3-y^3\) का गुणनखंड रूप क्या है?
What is the factorised form of \(125x^3-y^3\)?
#difference of cubes
#factorisation
#identity
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A ((5x-y)\(25x^2+5xy+y^2\))
B ((5x+y)\(25x^2-5xy+y^2\))
C ((125x-y)\(x^2+xy+y^2\))
D ((5x-y)\(25x^2-5xy+y^2\))
Explanation opens after your attempt
Correct Answer
A. ((5x-y)\(25x^2+5xy+y^2\))
Step 1
Concept
Since (125x-3 =(5x)3 ), this is a difference of cubes. Exam tip: keep (+5xy) in the second factor.
Step 2
Why this answer is correct
The correct answer is A. ((5x-y)\(25x^2+5xy+y^2\)). Since (125x-3 =(5x)3 ), this is a difference of cubes. Exam tip: keep (+5xy) in the second factor.
Step 3
Exam Tip
(125x-3 =(5x)3 ) है और यह घनों का अंतर है। परीक्षा में दूसरे गुणनखंड में (+5xy) रखें।
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\(x^2-2xy+y^2-z^2\) को गुणनखंडित करने का सही रूप कौन सा है?
Which is the correct factorised form of \(x^2-2xy+y^2-z^2\)?
#combined identities
#difference of squares
#factorisation
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A ((x-y-z)(x-y+z))
B ((x+y-z)(x+y+z))
C ((x-y)2 -z)
D ((x-z)(x+z)-2xy+y-2 )
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 ), then use difference of squares. Exam tip: form the perfect square first.
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 ), then use difference of squares. Exam tip: form the perfect square first.
Step 3
Exam Tip
पहले (x-2 -2xy+y-2 =(x-y)2 ), फिर अंतर के वर्ग लगाएं। परीक्षा में पहले पूर्ण वर्ग बनाएं।
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\(a^2+2ab+b^2-c^2\) के गुणनखंड क्या होंगे?
What will be the factors of \(a^2+2ab+b^2-c^2\)?
#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)
D ((a+c)(a-c)+2ab+b-2 )
Explanation opens after your attempt
Correct Answer
A. ((a+b-c)(a+b+c))
Step 1
Concept
First (a-2 +2ab+b-2 =(a+b)2 ), then take the difference with \(c^2\). Exam tip: solve mixed identities in two steps.
Step 2
Why this answer is correct
The correct answer is A. ((a+b-c)(a+b+c)). First (a-2 +2ab+b-2 =(a+b)2 ), then take the difference with \(c^2\). Exam tip: solve mixed identities in two steps.
Step 3
Exam Tip
पहले (a-2 +2ab+b-2 =(a+b)2 ), फिर \(c^2\) का अंतर लें। परीक्षा में मिश्रित पहचान को दो चरणों में हल करें।
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\(x^2-y^2+2x+1\) को किस रूप में गुणनखंडित किया जा सकता है?
In which form can \(x^2-y^2+2x+1\) be factorised?
#grouping
#perfect square
#difference of squares
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A ((x+1-y)(x+1+y))
B ((x-y)(x+y)+1)
C ((x+y+1)2 )
D ((x-1-y)(x-1+y))
Explanation opens after your attempt
Correct Answer
A. ((x+1-y)(x+1+y))
Step 1
Concept
Since (x-2 +2x+1=(x+1)2 ), the expression becomes ((x+1)2 -y-2 ). Exam tip: group terms correctly.
Step 2
Why this answer is correct
The correct answer is A. ((x+1-y)(x+1+y)). Since (x-2 +2x+1=(x+1)2 ), the expression becomes ((x+1)2 -y-2 ). Exam tip: group terms correctly.
Step 3
Exam Tip
(x-2 +2x+1=(x+1)2 ), इसलिए expression ((x+1)2 -y-2 ) बनती है। परीक्षा में पदों को सही समूह में रखें।
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\(4x^2+12x+9-y^2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form 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)(4x+9+y))
D ((2x+3)2 -y)
Explanation opens after your attempt
Correct Answer
A. ((2x+3-y)(2x+3+y))
Step 1
Concept
(4x-2 +12x+9=(2x+3)2 ). Exam tip: identify the perfect square first and then use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((2x+3-y)(2x+3+y)). (4x-2 +12x+9=(2x+3)2 ). Exam tip: identify the perfect square first and then use difference of squares.
Step 3
Exam Tip
(4x-2 +12x+9=(2x+3)2 ) है। परीक्षा में पहले पूर्ण वर्ग पहचानें फिर अंतर के वर्ग लगाएं।
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(2ab+3a+4b+6) का सही गुणनखंड रूप चुनिए।
Choose the correct factorised form of (2ab+3a+4b+6).
#grouping
#common binomial
#factorisation
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A ((a+2)(2b+3))
B ((a+4)(2b+3))
C ((2b+3)(a+2))
D ((2a+3)(b+2))
Explanation opens after your attempt
Correct Answer
C. ((2b+3)(a+2))
Step 1
Concept
Grouping gives (a(2b+3)+2(2b+3)). Exam tip: take out the common binomial.
Step 2
Why this answer is correct
The correct answer is C. ((2b+3)(a+2)). Grouping gives (a(2b+3)+2(2b+3)). Exam tip: take out the common binomial.
Step 3
Exam Tip
समूह करने पर (a(2b+3)+2(2b+3)) मिलता है। परीक्षा में समान द्विपद बाहर निकालें।
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(3xy-6x+5y-10) को समूह बनाकर गुणनखंडित करें।
Factorise (3xy-6x+5y-10) by grouping.
#factorisation by grouping
#common bracket
#algebra
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A ((3x+5)(y-2))
B ((3x-5)(y+2))
C ((y-2)(3x+5))
D ((3x-10)(y+5))
Explanation opens after your attempt
Correct Answer
A. ((3x+5)(y-2))
Step 1
Concept
(3x(y-2)+5(y-2)) gives the common bracket ((y-2)). Exam tip: keep grouping order correct.
Step 2
Why this answer is correct
The correct answer is A. ((3x+5)(y-2)). (3x(y-2)+5(y-2)) gives the common bracket ((y-2)). Exam tip: keep grouping order correct.
Step 3
Exam Tip
(3x(y-2)+5(y-2)) से समान कोष्ठक ((y-2)) बाहर आता है। परीक्षा में समूहों का क्रम सही रखें।
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\(x^2+2x-24\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+2x-24\)?
#trinomial factorisation
#signs
#quadratic
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A ((x+6)(x-4))
B ((x-6)(x+4))
C ((x+8)(x-3))
D ((x-8)(x+3))
Explanation opens after your attempt
Correct Answer
A. ((x+6)(x-4))
Step 1
Concept
(6+(-4)=2) and (6(-4)=-24). Exam tip: choose opposite signs for a negative last term.
Step 2
Why this answer is correct
The correct answer is A. ((x+6)(x-4)). (6+(-4)=2) and (6(-4)=-24). Exam tip: choose opposite signs for a negative last term.
Step 3
Exam Tip
(6+(-4)=2) और (6(-4)=-24) है। परीक्षा में ऋणात्मक अंतिम पद के लिए विपरीत चिन्ह चुनें।
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\(5x^2+13x-6\) के गुणनखंड कौन से हैं?
What are the factors of \(5x^2+13x-6\)?
#quadratic factorisation
#splitting
#checking
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A ((5x-2)(x+3))
B ((5x+3)(x-2))
C ((5x-3)(x+2))
D ((x-2)(5x+3))
Explanation opens after your attempt
Correct Answer
A. ((5x-2)(x+3))
Step 1
Concept
((5x-2)(x+3)) gives \(5x^2+15x-2x-6\). Exam tip: expand to check the middle term (13x).
Step 2
Why this answer is correct
The correct answer is A. ((5x-2)(x+3)). ((5x-2)(x+3)) gives \(5x^2+15x-2x-6\). Exam tip: expand to check the middle term (13x).
Step 3
Exam Tip
((5x-2)(x+3)) से \(5x^2+15x-2x-6\) मिलता है। परीक्षा में फैलाकर मध्य पद (13x) जांचें।
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\(7x^2-29x+12\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(7x^2-29x+12\)?
#hard quadratic
#factorisation
#signs
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A ((7x-3)(x-4))
B ((7x-4)(x-3))
C ((7x-12)(x-1))
D ((x-4)(7x-3))
Explanation opens after your attempt
Correct Answer
D. ((x-4)(7x-3))
Step 1
Concept
((x-4)(7x-3)) gives \(7x^2-3x-28x+12\). Exam tip: add both negative terms carefully.
Step 2
Why this answer is correct
The correct answer is D. ((x-4)(7x-3)). ((x-4)(7x-3)) gives \(7x^2-3x-28x+12\). Exam tip: add both negative terms carefully.
Step 3
Exam Tip
((x-4)(7x-3)) से \(7x^2-3x-28x+12\) मिलता है। परीक्षा में दोनों ऋणात्मक पदों का योग ध्यान से करें।
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\(x^2+6xy+9y^2-16z^2\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(x^2+6xy+9y^2-16z^2\)?
#mixed identity
#three variables
#factorisation
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A ((x+3y-4z)(x+3y+4z))
B ((x-3y-4z)(x-3y+4z))
C ((x+6y-16z)(x+6y+16z))
D ((x+3y)2 -4z)
Explanation opens after your attempt
Correct Answer
A. ((x+3y-4z)(x+3y+4z))
Step 1
Concept
First (x-2 +6xy+9y-2 =(x+3y)2 ), and (16z-2 =(4z)2 ). Exam tip: use two-step identities.
Step 2
Why this answer is correct
The correct answer is A. ((x+3y-4z)(x+3y+4z)). First (x-2 +6xy+9y-2 =(x+3y)2 ), and (16z-2 =(4z)2 ). Exam tip: use two-step identities.
Step 3
Exam Tip
पहले (x-2 +6xy+9y-2 =(x+3y)2 ), फिर (16z-2 =(4z)2 ) है। परीक्षा में दो चरणों वाली पहचान लगाएं।
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\(9a^2-12ab+4b^2-c^2\) को गुणनखंडित करें।
Factorise \(9a^2-12ab+4b^2-c^2\).
#perfect square
#difference of squares
#factorisation
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A ((3a-2b-c)(3a-2b+c))
B ((3a+2b-c)(3a+2b+c))
C ((9a-4b-c)(9a-4b+c))
D ((3a-2b)2 -c)
Explanation opens after your attempt
Correct Answer
A. ((3a-2b-c)(3a-2b+c))
Step 1
Concept
(9a-2 -12ab+4b-2 =(3a-2b)2 ). Exam tip: after the perfect square, use the difference with \(c^2\).
Step 2
Why this answer is correct
The correct answer is A. ((3a-2b-c)(3a-2b+c)). (9a-2 -12ab+4b-2 =(3a-2b)2 ). Exam tip: after the perfect square, use the difference with \(c^2\).
Step 3
Exam Tip
(9a-2 -12ab+4b-2 =(3a-2b)2 ) है। परीक्षा में पूर्ण वर्ग के बाद \(c^2\) का अंतर लगाएं।
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\(64r^3+125s^3\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(64r^3+125s^3\)?
#sum of cubes
#two variables
#factorisation
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A ((4r+5s)\(16r^2-20rs+25s^2\))
B ((4r-5s)\(16r^2+20rs+25s^2\))
C ((64r+125s)\(r^2-rs+s^2\))
D ((4r+5s)\(16r^2+20rs+25s^2\))
Explanation opens after your attempt
Correct Answer
A. ((4r+5s)\(16r^2-20rs+25s^2\))
Step 1
Concept
This is ((4r)3 +(5s)3 ). Exam tip: in sum of cubes, keep signs (+,-,+) in the second bracket.
Step 2
Why this answer is correct
The correct answer is A. ((4r+5s)\(16r^2-20rs+25s^2\)). This is ((4r)3 +(5s)3 ). Exam tip: in sum of cubes, keep signs (+,-,+) in the second bracket.
Step 3
Exam Tip
यह ((4r)3 +(5s)3 ) है। परीक्षा में घनों के योग में दूसरे कोष्ठक के चिन्ह (+,-,+) रखें।
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\(216x^3-27y^3\) को पहले सामान्य गुणनखंड निकालकर किस रूप में लिखा जा सकता है?
After taking out the common factor, how can \(216x^3-27y^3\) be written first?
#common factor
#cubes
#factorisation
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A (27\(8x^3-y^3\))
B (9\(24x^3-3y^3\))
C (3\(72x^3-9y^3\))
D (27\(6x^3-y^3\))
Explanation opens after your attempt
Correct Answer
A. (27\(8x^3-y^3\))
Step 1
Concept
Both terms have common factor (27), and \(216x^3=27\cdot8x^3\). Exam tip: taking out the common factor first makes it easier.
Step 2
Why this answer is correct
The correct answer is A. (27\(8x^3-y^3\)). Both terms have common factor (27), and \(216x^3=27\cdot8x^3\). Exam tip: taking out the common factor first makes it easier.
Step 3
Exam Tip
दोनों पदों में (27) सामान्य है और \(216x^3=27\cdot8x^3\) है। परीक्षा में पहले सामान्य गुणनखंड निकालना आसान करता है।
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\(216x^3-27y^3\) का पूर्ण गुणनखंड रूप क्या होगा?
What will be the complete factorised form of \(216x^3-27y^3\)?
#complete factorisation
#difference of cubes
#common factor
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A (27(2x-y)\(4x^2+2xy+y^2\))
B (27(2x+y)\(4x^2-2xy+y^2\))
C (27(8x-y)\(x^2+xy+y^2\))
D (27(2x-y)\(4x^2-2xy+y^2\))
Explanation opens after your attempt
Correct Answer
A. (27(2x-y)\(4x^2+2xy+y^2\))
Step 1
Concept
(216x-3 -27y-3 =27((2x)3 -y-3 )). Exam tip: use both common factor and difference of cubes.
Step 2
Why this answer is correct
The correct answer is A. (27(2x-y)\(4x^2+2xy+y^2\)). (216x-3 -27y-3 =27((2x)3 -y-3 )). Exam tip: use both common factor and difference of cubes.
Step 3
Exam Tip
(216x-3 -27y-3 =27((2x)3 -y-3 )) है। परीक्षा में सामान्य गुणनखंड और घनों के अंतर दोनों लगाएं।
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\(x^2+4xy+4y^2-25\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^2+4xy+4y^2-25\)?
#perfect square
#difference of squares
#factorisation
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A ((x+2y-5)(x+2y+5))
B ((x-2y-5)(x-2y+5))
C ((x+4y-25)(x+4y+25))
D ((x+2y)2 -5)
Explanation opens after your attempt
Correct Answer
A. ((x+2y-5)(x+2y+5))
Step 1
Concept
(x-2 +4xy+4y-2 =(x+2y)2 ) and \(25=5^2\). Exam tip: treat the perfect square as one unit.
Step 2
Why this answer is correct
The correct answer is A. ((x+2y-5)(x+2y+5)). (x-2 +4xy+4y-2 =(x+2y)2 ) and \(25=5^2\). Exam tip: treat the perfect square as one unit.
Step 3
Exam Tip
(x-2 +4xy+4y-2 =(x+2y)2 ) और \(25=5^2\) है। परीक्षा में पूर्ण वर्ग को एक इकाई मानें।
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\(4a^2-9b^2+4a+1\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(4a^2-9b^2+4a+1\)?
#rearrangement
#difference of squares
#factorisation
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A ((2a+1-3b)(2a+1+3b))
B ((2a-1-3b)(2a-1+3b))
C ((4a+1-9b)(4a+1+9b))
D ((2a+1)2 -3b)
Explanation opens after your attempt
Correct Answer
A. ((2a+1-3b)(2a+1+3b))
Step 1
Concept
(4a-2 +4a+1=(2a+1)2 ) and (9b-2 =(3b)2 ). Exam tip: rearrange terms first.
Step 2
Why this answer is correct
The correct answer is A. ((2a+1-3b)(2a+1+3b)). (4a-2 +4a+1=(2a+1)2 ) and (9b-2 =(3b)2 ). Exam tip: rearrange terms first.
Step 3
Exam Tip
(4a-2 +4a+1=(2a+1)2 ) और (9b-2 =(3b)2 ) है। परीक्षा में पहले पदों को पुनः क्रमबद्ध करें।
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\(x^2-4x-y^2+4\) को गुणनखंडित करने पर क्या मिलेगा?
What is obtained by factorising \(x^2-4x-y^2+4\)?
#perfect square
#difference of squares
#factorisation
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A ((x-2-y)(x-2+y))
B ((x+2-y)(x+2+y))
C ((x-y)(x+y)-4x+4)
D ((x-4-y)(x-4+y))
Explanation opens after your attempt
Correct Answer
A. ((x-2-y)(x-2+y))
Step 1
Concept
Since (x-2 -4x+4=(x-2)2 ), the expression becomes ((x-2)2 -y-2 ). Exam tip: use (+4) to form a perfect square.
Step 2
Why this answer is correct
The correct answer is A. ((x-2-y)(x-2+y)). Since (x-2 -4x+4=(x-2)2 ), the expression becomes ((x-2)2 -y-2 ). Exam tip: use (+4) to form a perfect square.
Step 3
Exam Tip
(x-2 -4x+4=(x-2)2 ), इसलिए expression ((x-2)2 -y-2 ) बनती है। परीक्षा में (+4) को पूर्ण वर्ग बनाने में उपयोग करें।
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\(a^4-16b^4\) का पूर्ण गुणनखंड रूप कौन सा है?
Which is the complete factorised form of \(a^4-16b^4\)?
#higher powers
#complete factorisation
#difference of squares
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A (\(a^2-4b^2\)\(a^2+4b^2\))
B ((a-2b)(a+2b)\(a^2+4b^2\))
C ((a-4b)(a+4b))
D ((a-2b)2 (a+2b)2 )
Explanation opens after your attempt
Correct Answer
B. ((a-2b)(a+2b)\(a^2+4b^2\))
Step 1
Concept
First (a-4 -16b-4 =\(a^2-4b^2\)\(a^2+4b^2\)), then \(a^2-4b^2\) factors further. Exam tip: stop only after complete factorisation.
Step 2
Why this answer is correct
The correct answer is B. ((a-2b)(a+2b)\(a^2+4b^2\)). First (a-4 -16b-4 =\(a^2-4b^2\)\(a^2+4b^2\)), then \(a^2-4b^2\) factors further. Exam tip: stop only after complete factorisation.
Step 3
Exam Tip
पहले (a-4 -16b-4 =\(a^2-4b^2\)\(a^2+4b^2\)), फिर \(a^2-4b^2\) टूटता है। परीक्षा में पूर्ण गुणनखंड तक रुकें।
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\(3x^2-14x+8\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(3x^2-14x+8\)?
#quadratic factorisation
#middle term
#signs
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A ((3x-2)(x-4))
B ((3x-8)(x-1))
C ((x-2)(3x-4))
D ((3x+2)(x-4))
Explanation opens after your attempt
Correct Answer
A. ((3x-2)(x-4))
Step 1
Concept
((3x-2)(x-4)) gives \(3x^2-12x-2x+8\). Exam tip: check the middle term (-14x).
Step 2
Why this answer is correct
The correct answer is A. ((3x-2)(x-4)). ((3x-2)(x-4)) gives \(3x^2-12x-2x+8\). Exam tip: check the middle term (-14x).
Step 3
Exam Tip
((3x-2)(x-4)) से \(3x^2-12x-2x+8\) मिलता है। परीक्षा में मध्य पद (-14x) जांचें।
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\(10x^2+x-3\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(10x^2+x-3\)?
#quadratic factorisation
#signs
#checking
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? Hint Small clue
A ((5x+3)(2x-1))
B ((5x-3)(2x+1))
C ((10x-3)(x+1))
D ((2x+3)(5x-1))
Explanation opens after your attempt
Correct Answer
A. ((5x+3)(2x-1))
Step 1
Concept
((5x+3)(2x-1)) gives \(10x^2-5x+6x-3\). Exam tip: identify the small difference for the middle term (x).
Step 2
Why this answer is correct
The correct answer is A. ((5x+3)(2x-1)). ((5x+3)(2x-1)) gives \(10x^2-5x+6x-3\). Exam tip: identify the small difference for the middle term (x).
Step 3
Exam Tip
((5x+3)(2x-1)) से \(10x^2-5x+6x-3\) मिलता है। परीक्षा में मध्य पद (x) के लिए छोटे अंतर को पहचानें।
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\(15x^2-2x-8\) के गुणनखंड कौन से हैं?
What are the factors of \(15x^2-2x-8\)?
#hard quadratic
#factorisation
#middle term
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? Hint Small clue
A ((3x+2)(5x-4))
B ((3x-2)(5x+4))
C ((15x+4)(x-2))
D ((5x+2)(3x-4))
Explanation opens after your attempt
Correct Answer
D. ((5x+2)(3x-4))
Step 1
Concept
((5x+2)(3x-4)) gives \(15x^2-20x+6x-8\). Exam tip: choose the pair that gives (-2x), not (-14x).
Step 2
Why this answer is correct
The correct answer is D. ((5x+2)(3x-4)). ((5x+2)(3x-4)) gives \(15x^2-20x+6x-8\). Exam tip: choose the pair that gives (-2x), not (-14x).
Step 3
Exam Tip
((5x+2)(3x-4)) से \(15x^2-20x+6x-8\) मिलता है। परीक्षा में (-14x) नहीं बल्कि (-2x) के लिए सही जोड़ी चुनें।
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\(2a^2+ab-15b^2\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(2a^2+ab-15b^2\)?
#two variable quadratic
#factorisation
#signs
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? Hint Small clue
A ((2a-5b)(a+3b))
B ((2a+5b)(a-3b))
C ((a+5b)(2a-3b))
D ((2a-3b)(a+5b))
Explanation opens after your attempt
Correct Answer
A. ((2a-5b)(a+3b))
Step 1
Concept
((2a-5b)(a+3b)) gives \(2a^2+6ab-5ab-15b^2\). Exam tip: check the sum of (ab)-terms.
Step 2
Why this answer is correct
The correct answer is A. ((2a-5b)(a+3b)). ((2a-5b)(a+3b)) gives \(2a^2+6ab-5ab-15b^2\). Exam tip: check the sum of (ab)-terms.
Step 3
Exam Tip
((2a-5b)(a+3b)) से \(2a^2+6ab-5ab-15b^2\) मिलता है। परीक्षा में (ab) पदों का योग जांचें।
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\(x^3-3x^2y+3xy^2-y^3\) किसका गुणनखंड रूप है?
Whose factorised form is \(x^3-3x^2y+3xy^2-y^3\)?
#cube of binomial
#factorisation
#identity
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A ((x-y)3 )
B ((x+y)3 )
C ((x-y)\(x^2+y^2\))
D ((x+y)\(x^2-xy+y^2\))
Explanation opens after your attempt
Correct Answer
A. ((x-y)3 )
Step 1
Concept
This is the identity of ((x-y)3 ). Exam tip: remember the sign pattern (+,-,+,-).
Step 2
Why this answer is correct
The correct answer is A. ((x-y)3 ). This is the identity of ((x-y)3 ). Exam tip: remember the sign pattern (+,-,+,-).
Step 3
Exam Tip
यह ((x-y)3 ) की पहचान है। परीक्षा में चिन्हों का क्रम (+,-,+,-) याद रखें।
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\(8x^3+12x^2y+6xy^2+y^3\) किस रूप में लिखा जाएगा?
In which form will \(8x^3+12x^2y+6xy^2+y^3\) be written?
#cube identity
#binomial cube
#factorisation
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? Hint Small clue
A ((2x-y)3 )
B ((2x+y)3 )
C ((8x+y)3 )
D ((x+2y)3 )
Explanation opens after your attempt
Correct Answer
B. ((2x+y)3 )
Step 1
Concept
It is of the form ((2x)3 +3(2x)2 y+3(2x)y-2 +y-3 ). Exam tip: identify the cube of a binomial.
Step 2
Why this answer is correct
The correct answer is B. ((2x+y)3 ). It is of the form ((2x)3 +3(2x)2 y+3(2x)y-2 +y-3 ). Exam tip: identify the cube of a binomial.
Step 3
Exam Tip
यह ((2x)3 +3(2x)2 y+3(2x)y-2 +y-3 ) का रूप है। परीक्षा में द्विपद के घन की पहचान करें।
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\(27a^3+54a^2b+36ab^2+8b^3\) किस रूप में लिखा जाएगा?
In which form will \(27a^3+54a^2b+36ab^2+8b^3\) be written?
#binomial cube
#factorisation
#algebraic identities
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A ((3a+2b)3 )
B ((3a-2b)3 )
C ((27a+8b)3 )
D ((a+2b)3 )
Explanation opens after your attempt
Correct Answer
A. ((3a+2b)3 )
Step 1
Concept
It is of the form ((3a)3 +3(3a)2 (2b)+3(3a)(2b)2 +(2b)3 ). Exam tip: match the (3AB) terms carefully in cube identities.
Step 2
Why this answer is correct
The correct answer is A. ((3a+2b)3 ). It is of the form ((3a)3 +3(3a)2 (2b)+3(3a)(2b)2 +(2b)3 ). Exam tip: match the (3AB) terms carefully in cube identities.
Step 3
Exam Tip
यह ((3a)3 +3(3a)2 (2b)+3(3a)(2b)2 +(2b)3 ) का रूप है। परीक्षा में घन पहचान में (3AB) वाले पदों को ध्यान से मिलाएं।
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\(x^4+2x^2y^2+y^4-16\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^4+2x^2y^2+y^4-16\)?
#mixed identities
#difference of squares
#factorisation
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A (\(x^2+y^2-4\)\(x^2+y^2+4\))
B (\(x^2-y^2-4\)\(x^2-y^2+4\))
C ((x+y-4)(x+y+4))
D (\(x^2+y^2\)2 -4)
Explanation opens after your attempt
Correct Answer
A. (\(x^2+y^2-4\)\(x^2+y^2+4\))
Step 1
Concept
First (x-4 +2x-2 y-2 +y-4 =\(x^2+y^2\)2 ), and then \(16=4^2\). Exam tip: solve mixed identities in two steps.
Step 2
Why this answer is correct
The correct answer is A. (\(x^2+y^2-4\)\(x^2+y^2+4\)). First (x-4 +2x-2 y-2 +y-4 =\(x^2+y^2\)2 ), and then \(16=4^2\). Exam tip: solve mixed identities in two steps.
Step 3
Exam Tip
पहले (x-4 +2x-2 y-2 +y-4 =\(x^2+y^2\)2 ), फिर \(16=4^2\) है। परीक्षा में मिश्रित पहचान को दो चरणों में हल करें।
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