\(x^4-16\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(x^4-16\)?
#difference of squares
#complete factorisation
#algebraic identities
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A ( (x-2)(x+2)\(x^2+4\) )
B ( \(x^2-4\)\(x^2+4\) )
C ( (x-4)(x+4)\(x^2+1\) )
D ( (x-2)2 (x+2)2 )
Explanation opens after your attempt
Correct Answer
A. ( (x-2)(x+2)\(x^2+4\) )
Step 1
Concept
First write \(x^4-16\) as (\(x^2\)2 -42 ) and then factor \(x^2-4\). Exam tip: do not stop before the complete factorisation.
Step 2
Why this answer is correct
The correct answer is A. ( (x-2)(x+2)\(x^2+4\) ). First write \(x^4-16\) as (\(x^2\)2 -42 ) and then factor \(x^2-4\). Exam tip: do not stop before the complete factorisation.
Step 3
Exam Tip
पहले \(x^4-16\) को (\(x^2\)2 -42 ) लिखें और फिर \(x^2-4\) को भी तोड़ें। परीक्षा में पूर्ण गुणनखंड रूप तक रुकें नहीं।
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\(a^4-b^4\) का पूर्ण गुणनखंड रूप चुनिए।
Choose the complete factorisation of \(a^4-b^4\).
#difference of fourth powers
#factorisation
#identity
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A ( \(a^2-b^2\)\(a^2+b^2\) )
B ( (a-b)2 (a+b)2 )
C ( (a-b)(a+b)\(a^2+b^2\) )
D ( (a-b)\(a^3+b^3\) )
Explanation opens after your attempt
Correct Answer
C. ( (a-b)(a+b)\(a^2+b^2\) )
Step 1
Concept
In \(a^4-b^4\), first use difference of squares and then factor \(a^2-b^2\). Exam tip: \(a^2+b^2\) is usually not factored further here.
Step 2
Why this answer is correct
The correct answer is C. ( (a-b)(a+b)\(a^2+b^2\) ). In \(a^4-b^4\), first use difference of squares and then factor \(a^2-b^2\). Exam tip: \(a^2+b^2\) is usually not factored further here.
Step 3
Exam Tip
\(a^4-b^4\) में पहले अंतर वर्ग और फिर \(a^2-b^2\) का गुणनखंडन करें। परीक्षा में \(a^2+b^2\) को सामान्यतः आगे नहीं तोड़ा जाता।
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\(x^2+2xy+y^2-9z^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(x^2+2xy+y^2-9z^2\)?
#mixed identity
#perfect square
#difference of squares
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A ( (x-y-3z)(x-y+3z) )
B ( (x+y-3z)(x+y+3z) )
C ( (x+y-9z)(x+y+z) )
D ( (x+y+3z)2 )
Explanation opens after your attempt
Correct Answer
B. ( (x+y-3z)(x+y+3z) )
Step 1
Concept
First convert \(x^2+2xy+y^2\) into ((x+y)2 ). Exam tip: after forming a perfect square, apply difference of squares.
Step 2
Why this answer is correct
The correct answer is B. ( (x+y-3z)(x+y+3z) ). First convert \(x^2+2xy+y^2\) into ((x+y)2 ). Exam tip: after forming a perfect square, apply difference of squares.
Step 3
Exam Tip
पहले \(x^2+2xy+y^2\) को ((x+y)2 ) बनाएं। परीक्षा में पूर्ण वर्ग के बाद अंतर वर्ग लगाएं।
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\(4p^2-12pq+9q^2-25r^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(4p^2-12pq+9q^2-25r^2\)?
#perfect square
#difference of squares
#factorisation
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A ( (2p+3q-5r)(2p+3q+5r) )
B ( (2p-3q)2 -25r-2 )
C ( (4p-9q-25r)(p+q+r) )
D ( (2p-3q-5r)(2p-3q+5r) )
Explanation opens after your attempt
Correct Answer
D. ( (2p-3q-5r)(2p-3q+5r) )
Step 1
Concept
First write \(4p^2-12pq+9q^2\) as ((2p-3q)2 ). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is D. ( (2p-3q-5r)(2p-3q+5r) ). First write \(4p^2-12pq+9q^2\) as ((2p-3q)2 ). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 3
Exam Tip
पहले \(4p^2-12pq+9q^2\) को ((2p-3q)2 ) लिखें। परीक्षा में ऋणात्मक मध्य पद से ((a-b)2 ) पहचानें।
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(x-3 -8y-3 +6xy(x-2y)) का गुणनखंड रूप चुनिए।
Choose the factorised form of (x-3 -8y-3 +6xy(x-2y)).
#difference of cubes
#common factor
#factorisation
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A ( (x-2y)(x+2y)2 )
B ( (x+2y)(x-2y)2 )
C ( (x-2y)\(x^2+2xy+4y^2\) )
D ( (x+2y)\(x^2-2xy+4y^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (x-2y)(x+2y)2 )
Step 1
Concept
Write \(x^3-8y^3\) as ((x-2y)\(x^2+2xy+4y^2\)) and take the common factor. Exam tip: identify the common binomial first.
Step 2
Why this answer is correct
The correct answer is A. ( (x-2y)(x+2y)2 ). Write \(x^3-8y^3\) as ((x-2y)\(x^2+2xy+4y^2\)) and take the common factor. Exam tip: identify the common binomial first.
Step 3
Exam Tip
\(x^3-8y^3\) को ((x-2y)\(x^2+2xy+4y^2\)) लिखकर समान गुणनखंड लें। परीक्षा में पहले सामान्य द्विपद पहचानें।
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\(2x^2+7xy+3y^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(2x^2+7xy+3y^2\)?
#quadratic in two variables
#middle term
#factorisation
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A ( (2x+3y)(x+y) )
B ( (2x+y)(x+3y) )
C ( (x+2y)(2x+3y) )
D ( (2x-y)(x-3y) )
Explanation opens after your attempt
Correct Answer
B. ( (2x+y)(x+3y) )
Step 1
Concept
Split the middle term (7xy) as (6xy+xy). Exam tip: choose the pair with product (6) and sum (7).
Step 2
Why this answer is correct
The correct answer is B. ( (2x+y)(x+3y) ). Split the middle term (7xy) as (6xy+xy). Exam tip: choose the pair with product (6) and sum (7).
Step 3
Exam Tip
मध्य पद (7xy) को (6xy+xy) में तोड़ें। परीक्षा में ((2)(3)=6) और योग (7) वाली जोड़ी चुनें।
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\(6x^2-x-12\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(6x^2-x-12\)?
#quadratic
#signs
#factorisation
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A ( (3x-4)(2x+3) )
B ( (6x-4)(x+3) )
C ( (3x+4)(2x-3) )
D ( (2x-4)(3x+3) )
Explanation opens after your attempt
Correct Answer
C. ( (3x+4)(2x-3) )
Step 1
Concept
Expanding gives ( (3x+4)(2x-3)=6x-2 -x-12 ). Exam tip: verify by expansion when signs are tricky.
Step 2
Why this answer is correct
The correct answer is C. ( (3x+4)(2x-3) ). Expanding gives ( (3x+4)(2x-3)=6x-2 -x-12 ). Exam tip: verify by expansion when signs are tricky.
Step 3
Exam Tip
फैलाने पर ( (3x+4)(2x-3)=6x-2 -x-12 ) मिलता है। परीक्षा में कठिन चिन्हों वाले प्रश्न में विस्तार से जांच करें।
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\(12a^2-7ab-b^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(12a^2-7ab-b^2\).
#quadratic in variables
#ac method
#factorisation
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A ( (3a+b)(4a-b) )
B ( (12a+b)(a-b) )
C ( (3a-b)(4a+b) )
D ( (4a- b)(3a+b) )
Explanation opens after your attempt
Correct Answer
D. ( (4a- b)(3a+b) )
Step 1
Concept
For (-7ab), write \(12a^2-8ab+ab-b^2\). Exam tip: when options look similar, confirm by expansion.
Step 2
Why this answer is correct
The correct answer is D. ( (4a- b)(3a+b) ). For (-7ab), write \(12a^2-8ab+ab-b^2\). Exam tip: when options look similar, confirm by expansion.
Step 3
Exam Tip
(-7ab) के लिए \(12a^2-8ab+ab-b^2\) बनता है। परीक्षा में विकल्प समान दिखें तो फैलाकर पुष्टि करें।
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\(x^4+5x^2+6\) को गुणनखंडों में बदलें।
Convert \(x^4+5x^2+6\) into factors.
#biquadratic
#factorisation
#substitution
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A ( \(x^2+1\)\(x^2+6\) )
B ( \(x^2+2\)\(x^2+3\) )
C ( (x+2)(x+3) )
D ( \(x^2-2\)\(x^2-3\) )
Explanation opens after your attempt
Correct Answer
B. ( \(x^2+2\)\(x^2+3\) )
Step 1
Concept
Treat \(x^2\) as a new term and factor like a quadratic. Exam tip: for \(x^4\) type questions, think \(u=x^2\).
Step 2
Why this answer is correct
The correct answer is B. ( \(x^2+2\)\(x^2+3\) ). Treat \(x^2\) as a new term and factor like a quadratic. Exam tip: for \(x^4\) type questions, think \(u=x^2\).
Step 3
Exam Tip
\(x^2\) को एक नया पद मानकर द्विघात की तरह गुणनखंड करें। परीक्षा में \(x^4\) वाले प्रश्न को \(u=x^2\) सोचकर हल करें।
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\(y^4-13y^2+36\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(y^4-13y^2+36\)?
#biquadratic
#middle term
#factorisation
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A ( \(y^2-4\)\(y^2-9\) )
B ( \(y^2+4\)\(y^2+9\) )
C ( (y-4)(y-9) )
D ( \(y^2-6\)\(y^2-6\) )
Explanation opens after your attempt
Correct Answer
A. ( \(y^2-4\)\(y^2-9\) )
Step 1
Concept
Taking \(y^2\) as one quantity, the product must be (36) and the sum (-13). Exam tip: identify the pair (-4) and (-9).
Step 2
Why this answer is correct
The correct answer is A. ( \(y^2-4\)\(y^2-9\) ). Taking \(y^2\) as one quantity, the product must be (36) and the sum (-13). Exam tip: identify the pair (-4) and (-9).
Step 3
Exam Tip
\(y^2\) को एक मात्रा मानने पर गुणनफल (36) और योग (-13) चाहिए। परीक्षा में (-4) और (-9) की जोड़ी पहचानें।
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\(a^2+4b^2+9c^2+4ab+12bc+6ac\) का गुणनखंड रूप क्या है?
What is the factorised form of \(a^2+4b^2+9c^2+4ab+12bc+6ac\)?
#perfect square trinomial
#three variables
#factorisation
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A ( (a+2b-3c)2 )
B ( (a-2b+3c)2 )
C ( (a+2b+3c)2 )
D ( (a+4b+9c)2 )
Explanation opens after your attempt
Correct Answer
C. ( (a+2b+3c)2 )
Step 1
Concept
All middle terms form (2ab)-type pairs of (a), (2b), and (3c). Exam tip: check a three-term square pairwise.
Step 2
Why this answer is correct
The correct answer is C. ( (a+2b+3c)2 ). All middle terms form (2ab)-type pairs of (a), (2b), and (3c). Exam tip: check a three-term square pairwise.
Step 3
Exam Tip
सभी मध्य पद (2ab) प्रकार से (a), (2b), (3c) के जोड़े बनाते हैं। परीक्षा में तीन पदों वाले पूर्ण वर्ग को जोड़ीवार जांचें।
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\(m^2+n^2+p^2-2mn-2np+2mp\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(m^2+n^2+p^2-2mn-2np+2mp\)?
#perfect square
#three terms
#signs
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A ( (m+n+p)2 )
B ( (m-n-p)2 )
C ( (m-n+p)2 )
D ( (m+n-p)2 )
Explanation opens after your attempt
Correct Answer
C. ( (m-n+p)2 )
Step 1
Concept
This is the perfect square of (m), (-n), and (p). Exam tip: decide bracket signs from the signs of mixed terms.
Step 2
Why this answer is correct
The correct answer is C. ( (m-n+p)2 ). This is the perfect square of (m), (-n), and (p). Exam tip: decide bracket signs from the signs of mixed terms.
Step 3
Exam Tip
यह (m), (-n), (p) का पूर्ण वर्ग है। परीक्षा में मिश्रित पदों के चिन्ह से ब्रैकेट के चिन्ह तय करें।
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\(x^2+4x-45\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+4x-45\).
#quadratic
#sign choice
#factorisation
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A ( (x+9)(x-5) )
B ( (x-9)(x+5) )
C ( (x+15)(x-3) )
D ( (x-1)(x+45) )
Explanation opens after your attempt
Correct Answer
A. ( (x+9)(x-5) )
Step 1
Concept
The numbers (9) and (-5) have sum (4) and product (-45). Exam tip: with opposite signs, the larger magnitude gives the middle term sign.
Step 2
Why this answer is correct
The correct answer is A. ( (x+9)(x-5) ). The numbers (9) and (-5) have sum (4) and product (-45). Exam tip: with opposite signs, the larger magnitude gives the middle term sign.
Step 3
Exam Tip
(9) और (-5) का योग (4) और गुणनफल (-45) है। परीक्षा में अलग चिन्हों में बड़े परिमाण का चिन्ह मध्य पद देता है।
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\(3x^2-17x+10\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(3x^2-17x+10\)?
#quadratic
#ac method
#factorisation
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A ( (3x-10)(x-1) )
B ( (3x-2)(x-5) )
C ( (3x+2)(x+5) )
D ( (x-10)(3x-1) )
Explanation opens after your attempt
Correct Answer
B. ( (3x-2)(x-5) )
Step 1
Concept
Expanding gives ( (3x-2)(x-5)=3x-2 -17x+10 ). Exam tip: choose the pair with product (30) and sum (-17).
Step 2
Why this answer is correct
The correct answer is B. ( (3x-2)(x-5) ). Expanding gives ( (3x-2)(x-5)=3x-2 -17x+10 ). Exam tip: choose the pair with product (30) and sum (-17).
Step 3
Exam Tip
फैलाने पर ( (3x-2)(x-5)=3x-2 -17x+10 ) मिलता है। परीक्षा में (ac=30) और योग (-17) वाली जोड़ी लें।
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\(5u^2+13uv-6v^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(5u^2+13uv-6v^2\)?
#quadratic in variables
#middle term
#factorisation
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A ( (5u-2v)(u+3v) )
B ( (5u+2v)(u-3v) )
C ( (5u-2v)(u+3v) )
D ( (u+6v)(5u-v) )
Explanation opens after your attempt
Correct Answer
C. ( (5u-2v)(u+3v) )
Step 1
Concept
The split (15uv-2uv) gives the middle term (13uv). Exam tip: for a negative last term, check opposite signs.
Step 2
Why this answer is correct
The correct answer is C. ( (5u-2v)(u+3v) ). The split (15uv-2uv) gives the middle term (13uv). Exam tip: for a negative last term, check opposite signs.
Step 3
Exam Tip
(15uv-2uv) से मध्य पद (13uv) बनता है। परीक्षा में ऋणात्मक अंतिम पद के लिए विपरीत चिन्हों की जांच करें।
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\(7a^2-5ab-2b^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(7a^2-5ab-2b^2\).
#quadratic in variables
#verification
#factorisation
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A ( (7a+2b)(a-b) )
B ( (7a-b)(a+2b) )
C ( (7a-2b)(a+b) )
D ( (7a+2b)(a-b) )
Explanation opens after your attempt
Correct Answer
D. ( (7a+2b)(a-b) )
Step 1
Concept
Expanding gives \(7a^2-7ab+2ab-2b^2\). Exam tip: verify similar-looking options by expansion.
Step 2
Why this answer is correct
The correct answer is D. ( (7a+2b)(a-b) ). Expanding gives \(7a^2-7ab+2ab-2b^2\). Exam tip: verify similar-looking options by expansion.
Step 3
Exam Tip
फैलाने पर \(7a^2-7ab+2ab-2b^2\) मिलता है। परीक्षा में समान दिखने वाले विकल्पों को विस्तार से जांचें।
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\(x^3+y^3+z^3-3xyz\) में यदि (x+y+z) गुणनखंड है, तो दूसरा गुणनखंड क्या होगा?
If (x+y+z) is a factor of \(x^3+y^3+z^3-3xyz\), what is the other factor?
#cubic identity
#three variables
#factorisation
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A \( x^2+y^2+z^2-xy-yz-zx \)
B \( x^2+y^2+z^2+xy+yz+zx \)
C \( x^2-y^2+z^2 \)
D ( x+y+z )
Explanation opens after your attempt
Correct Answer
A. \( x^2+y^2+z^2-xy-yz-zx \)
Step 1
Concept
This is the identity (x-3 +y-3 +z-3 -3xyz=(x+y+z)\(x^2+y^2+z^2-xy-yz-zx\)). Exam tip: remember the three-variable cubic identity.
Step 2
Why this answer is correct
The correct answer is A. \( x^2+y^2+z^2-xy-yz-zx \). This is the identity (x-3 +y-3 +z-3 -3xyz=(x+y+z)\(x^2+y^2+z^2-xy-yz-zx\)). Exam tip: remember the three-variable cubic identity.
Step 3
Exam Tip
यह प्रसिद्ध पहचान (x-3 +y-3 +z-3 -3xyz=(x+y+z)\(x^2+y^2+z^2-xy-yz-zx\)) है। परीक्षा में तीन चर वाली घन पहचान याद रखें।
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यदि (x+y+z=0), तो \(x^3+y^3+z^3\) किसके बराबर होगा?
If (x+y+z=0), then \(x^3+y^3+z^3\) will be equal to what?
#cubic identity
#condition
#factorisation
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A ( xyz )
B ( 3xyz )
C \( x^2+y^2+z^2 \)
D ( 0 )
Explanation opens after your attempt
Correct Answer
B. ( 3xyz )
Step 1
Concept
The identity gives \(x^3+y^3+z^3-3xyz=0\). Exam tip: when (x+y+z=0), remember (3xyz).
Step 2
Why this answer is correct
The correct answer is B. ( 3xyz ). The identity gives \(x^3+y^3+z^3-3xyz=0\). Exam tip: when (x+y+z=0), remember (3xyz).
Step 3
Exam Tip
पहचान से \(x^3+y^3+z^3-3xyz=0\) मिलता है। परीक्षा में शर्त (x+y+z=0) मिलते ही (3xyz) याद करें।
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\(64x^3+125y^3+216z^3-180xyz\) किस रूप में लिखा जा सकता है?
How can \(64x^3+125y^3+216z^3-180xyz\) be written?
#cubic identity
#three variables
#advanced factorisation
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A ( (4x+5y+6z)\(16x^2+25y^2+36z^2-20xy-30yz-24xz\) )
B ( (4x-5y+6z)\(16x^2+25y^2+36z^2\) )
C ( (4x+5y-6z)3 )
D ( (8x+25y+36z)\(x^2+y^2+z^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (4x+5y+6z)\(16x^2+25y^2+36z^2-20xy-30yz-24xz\) )
Step 1
Concept
It is ( (4x)3 +(5y)3 +(6z)3 -3(4x)(5y)(6z) ). Exam tip: apply the identity \(a^3+b^3+c^3-3abc\).
Step 2
Why this answer is correct
The correct answer is A. ( (4x+5y+6z)\(16x^2+25y^2+36z^2-20xy-30yz-24xz\) ). It is ( (4x)3 +(5y)3 +(6z)3 -3(4x)(5y)(6z) ). Exam tip: apply the identity \(a^3+b^3+c^3-3abc\).
Step 3
Exam Tip
यह ( (4x)3 +(5y)3 +(6z)3 -3(4x)(5y)(6z) ) है। परीक्षा में \(a^3+b^3+c^3-3abc\) पहचान लागू करें।
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\(x^2-6xy+9y^2-16z^2\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(x^2-6xy+9y^2-16z^2\)?
#perfect square
#difference of squares
#factorisation
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A ( (x+3y-4z)(x+3y+4z) )
B ( (x-3y-4z)(x-3y+4z) )
C ( (x-6y-16z)(x+y+z) )
D ( (x-3y+4z)2 )
Explanation opens after your attempt
Correct Answer
B. ( (x-3y-4z)(x-3y+4z) )
Step 1
Concept
First write \(x^2-6xy+9y^2\) as ((x-3y)2 ). Exam tip: then use (16z-2 =(4z)2 ).
Step 2
Why this answer is correct
The correct answer is B. ( (x-3y-4z)(x-3y+4z) ). First write \(x^2-6xy+9y^2\) as ((x-3y)2 ). Exam tip: then use (16z-2 =(4z)2 ).
Step 3
Exam Tip
पहले \(x^2-6xy+9y^2\) को ((x-3y)2 ) बनाएं। परीक्षा में उसके बाद (16z-2 =(4z)2 ) लगाएं।
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\(2x^3+16\) का पूर्ण गुणनखंड रूप चुनिए।
Choose the complete factorised form of \(2x^3+16\).
#common factor
#sum of cubes
#factorisation
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A ( 2(x+2)\(x^2-2x+4\) )
B ( (2x+16)\(x^2-2x+4\) )
C ( 2(x-2)\(x^2+2x+4\) )
D ( (x+2)\(2x^2-4x+8\) )
Explanation opens after your attempt
Correct Answer
A. ( 2(x+2)\(x^2-2x+4\) )
Step 1
Concept
First take out common factor (2) and apply sum of cubes to \(x^3+8\). Exam tip: do not forget the common factor.
Step 2
Why this answer is correct
The correct answer is A. ( 2(x+2)\(x^2-2x+4\) ). First take out common factor (2) and apply sum of cubes to \(x^3+8\). Exam tip: do not forget the common factor.
Step 3
Exam Tip
पहले (2) सार्व गुणनखंड निकालें और \(x^3+8\) पर घनों का योग लगाएं। परीक्षा में सार्व गुणनखंड को अलग रखना न भूलें।
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\(81a^4-16b^4\) का पूर्ण गुणनखंड क्या है?
What is the complete factorisation of \(81a^4-16b^4\)?
#difference of fourth powers
#complete factorisation
#identity
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A ( \(9a^2-4b^2\)\(9a^2+4b^2\) )
B ( (3a-2b)(3a+2b)\(9a^2+4b^2\) )
C ( (9a-4b)(9a+4b) )
D ( (3a-2b)2 (3a+2b)2 )
Explanation opens after your attempt
Correct Answer
B. ( (3a-2b)(3a+2b)\(9a^2+4b^2\) )
Step 1
Concept
Here (81a-4 =\(9a^2\)2 ) and (16b-4 =\(4b^2\)2 ). Exam tip: factor \(9a^2-4b^2\) further too.
Step 2
Why this answer is correct
The correct answer is B. ( (3a-2b)(3a+2b)\(9a^2+4b^2\) ). Here (81a-4 =\(9a^2\)2 ) and (16b-4 =\(4b^2\)2 ). Exam tip: factor \(9a^2-4b^2\) further too.
Step 3
Exam Tip
(81a-4 =\(9a^2\)2 ) और (16b-4 =\(4b^2\)2 ) हैं। परीक्षा में \(9a^2-4b^2\) को आगे भी तोड़ें।
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\(x^4-10x^2+9\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(x^4-10x^2+9\)?
#biquadratic
#complete factorisation
#difference of squares
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A ( \(x^2-1\)\(x^2-9\) )
B ( \(x^2+1\)\(x^2+9\) )
C ( (x-1)(x+1)(x-3)(x+3) )
D ( \(x^2-3\)2 )
Explanation opens after your attempt
Correct Answer
C. ( (x-1)(x+1)(x-3)(x+3) )
Step 1
Concept
First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 2
Why this answer is correct
The correct answer is C. ( (x-1)(x+1)(x-3)(x+3) ). First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 3
Exam Tip
पहले (\(x^2-1\)\(x^2-9\)) मिलता है और दोनों अंतर वर्ग हैं। परीक्षा में पूर्ण गुणनखंड रूप के लिए अंतिम तक तोड़ें।
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\(9x^2+30xy+25y^2-49z^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(9x^2+30xy+25y^2-49z^2\).
#perfect square
#difference of squares
#factorisation
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A ( (3x-5y-7z)(3x-5y+7z) )
B ( (9x+25y-49z)(x+y+z) )
C ( (3x+5y+7z)2 )
D ( (3x+5y-7z)(3x+5y+7z) )
Explanation opens after your attempt
Correct Answer
D. ( (3x+5y-7z)(3x+5y+7z) )
Step 1
Concept
First write \(9x^2+30xy+25y^2\) as ((3x+5y)2 ). Exam tip: use (49z-2 =(7z)2 ) for difference of squares.
Step 2
Why this answer is correct
The correct answer is D. ( (3x+5y-7z)(3x+5y+7z) ). First write \(9x^2+30xy+25y^2\) as ((3x+5y)2 ). Exam tip: use (49z-2 =(7z)2 ) for difference of squares.
Step 3
Exam Tip
पहले \(9x^2+30xy+25y^2\) को ((3x+5y)2 ) बनाएं। परीक्षा में (49z-2 =(7z)2 ) से अंतर वर्ग लगाएं।
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(ab(a-b)+bc(b-c)+ca(c-a)) का गुणनखंड रूप क्या है?
What is the factorised form of (ab(a-b)+bc(b-c)+ca(c-a))?
#cyclic expression
#factorisation
#advanced algebra
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A ( -(a-b)(b-c)(c-a) )
B ( (a+b+c)(ab+bc+ca) )
C ( (a-b)(b-c)(c-a) )
D ( abc(a-b-c) )
Explanation opens after your attempt
Correct Answer
A. ( -(a-b)(b-c)(c-a) )
Step 1
Concept
Expanding and grouping the terms gives (-(a-b)(b-c)(c-a)). Exam tip: handle signs carefully in cyclic expressions.
Step 2
Why this answer is correct
The correct answer is A. ( -(a-b)(b-c)(c-a) ). Expanding and grouping the terms gives (-(a-b)(b-c)(c-a)). Exam tip: handle signs carefully in cyclic expressions.
Step 3
Exam Tip
विस्तार करके पदों को समूहित करने पर (-(a-b)(b-c)(c-a)) मिलता है। परीक्षा में चक्रीय पदों में चिन्ह बहुत ध्यान से रखें।
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\(x^2+2x+1-y^2-4y-4\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(x^2+2x+1-y^2-4y-4\)?
#difference of squares
#completion
#factorisation
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A ( (x-y-1)(x+y+3) )
B ( (x-y+1)(x+y-3) )
C ( (x+y+1)(x-y-3) )
D ( (x+1-y-2)(x+1+y+2) )
Explanation opens after your attempt
Correct Answer
A. ( (x-y-1)(x+y+3) )
Step 1
Concept
Write it as ((x+1)2 -(y+2)2 ). On simplifying, we get ((x-y-1)(x+y+3)).
Step 2
Why this answer is correct
The correct answer is A. ( (x-y-1)(x+y+3) ). Write it as ((x+1)2 -(y+2)2 ). On simplifying, we get ((x-y-1)(x+y+3)).
Step 3
Exam Tip
इसे ((x+1)2 -(y+2)2 ) लिखें। सरल करने पर ((x-y-1)(x+y+3)) मिलता है।
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\(4x^2+4xy+y^2-6x-3y\) का गुणनखंड रूप क्या है?
What is the factorised form of \(4x^2+4xy+y^2-6x-3y\)?
#perfect square
#common factor
#factorisation
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A ( (2x+y)(2x+y+3) )
B ( (2x+y)(2x+y-3) )
C ( (2x-y)(2x-y-3) )
D ( (4x+y)(x+y-3) )
Explanation opens after your attempt
Correct Answer
B. ( (2x+y)(2x+y-3) )
Step 1
Concept
First write (4x-2 +4xy+y-2 =(2x+y)2 ). Then take ((2x+y)) as the common factor.
Step 2
Why this answer is correct
The correct answer is B. ( (2x+y)(2x+y-3) ). First write (4x-2 +4xy+y-2 =(2x+y)2 ). Then take ((2x+y)) as the common factor.
Step 3
Exam Tip
पहले (4x-2 +4xy+y-2 =(2x+y)2 ) लिखें। फिर ((2x+y)) को सार्व गुणनखंड लें।
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\(x^2-y^2+4x+4\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-y^2+4x+4\).
#completion
#difference of squares
#factorisation
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A ( (x+y+2)(x-y+2) )
B ( (x-y+4)(x+y) )
C ( (x+2-y)(x+2+y) )
D ( (x+y-2)(x-y-2) )
Explanation opens after your attempt
Correct Answer
C. ( (x+2-y)(x+2+y) )
Step 1
Concept
Write it in the form ((x+2)2 -y-2 ). Exam tip: completing the square-like part is useful.
Step 2
Why this answer is correct
The correct answer is C. ( (x+2-y)(x+2+y) ). Write it in the form ((x+2)2 -y-2 ). Exam tip: completing the square-like part is useful.
Step 3
Exam Tip
इसे ((x+2)2 -y-2 ) के रूप में लिखें। परीक्षा में अपूर्ण वर्ग को पूरा करना उपयोगी होता है।
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\(25x^2-20xy+4y^2-36\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(25x^2-20xy+4y^2-36\)?
#perfect square
#difference of squares
#factorisation
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A ( (5x-2y-6)(5x-2y+6) )
B ( (5x+2y-6)(5x+2y+6) )
C ( (25x-4y-36)(x+y+1) )
D ( (5x-2y+6)2 )
Explanation opens after your attempt
Correct Answer
A. ( (5x-2y-6)(5x-2y+6) )
Step 1
Concept
First write \(25x^2-20xy+4y^2\) as ((5x-2y)2 ). Exam tip: use \(36=6^2\) for difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ( (5x-2y-6)(5x-2y+6) ). First write \(25x^2-20xy+4y^2\) as ((5x-2y)2 ). Exam tip: use \(36=6^2\) for difference of squares.
Step 3
Exam Tip
पहले \(25x^2-20xy+4y^2\) को ((5x-2y)2 ) बनाएं। परीक्षा में \(36=6^2\) से अंतर वर्ग लागू करें।
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\(16a^4-81b^4\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(16a^4-81b^4\)?
#difference of fourth powers
#complete factorisation
#identity
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A ( \(4a^2-9b^2\)\(4a^2+9b^2\) )
B ( (2a-3b)(2a+3b)\(4a^2+9b^2\) )
C ( (4a-9b)(4a+9b) )
D ( (2a-3b)2 (2a+3b)2 )
Explanation opens after your attempt
Correct Answer
B. ( (2a-3b)(2a+3b)\(4a^2+9b^2\) )
Step 1
Concept
First write \(16a^4-81b^4\) as (\(4a^2\)2 -\(9b^2\)2 ). Then factor \(4a^2-9b^2\) further.
Step 2
Why this answer is correct
The correct answer is B. ( (2a-3b)(2a+3b)\(4a^2+9b^2\) ). First write \(16a^4-81b^4\) as (\(4a^2\)2 -\(9b^2\)2 ). Then factor \(4a^2-9b^2\) further.
Step 3
Exam Tip
पहले \(16a^4-81b^4\) को (\(4a^2\)2 -\(9b^2\)2 ) लिखें। फिर \(4a^2-9b^2\) को आगे तोड़ें।
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\(x^2+7x+12-y^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+7x+12-y^2\).
#mixed factorisation
#verification
#quadratic
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A ( (x+3-y)(x+4+y) )
B ( (x+3+y)(x+4-y) )
C ( (x+3-y)(x+4+y) )
D ( (x+y+3)(x+y+4) )
Explanation opens after your attempt
Correct Answer
C. ( (x+3-y)(x+4+y) )
Step 1
Concept
Factoring \(x^2+7x+12\) as ((x+3)(x+4)) alone is not enough. Expanding the given option also gives the term \(-y^2\).
Step 2
Why this answer is correct
The correct answer is C. ( (x+3-y)(x+4+y) ). Factoring \(x^2+7x+12\) as ((x+3)(x+4)) alone is not enough. Expanding the given option also gives the term \(-y^2\).
Step 3
Exam Tip
\(x^2+7x+12\) को ((x+3)(x+4)) तोड़ना पर्याप्त नहीं है। दिए गए विकल्प को फैलाने पर सही पद \( -y^2 \) भी मिलता है।
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\(a^2+b^2+c^2+2ab-2ac-2bc\) का गुणनखंड रूप क्या है?
What is the factorised form of \(a^2+b^2+c^2+2ab-2ac-2bc\)?
#perfect square
#three variables
#signs
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A ( (a-b-c)2 )
B ( (a+b+c)2 )
C ( (a-b+c)2 )
D ( (a+b-c)2 )
Explanation opens after your attempt
Correct Answer
D. ( (a+b-c)2 )
Step 1
Concept
This is the perfect square of (a), (b), and (-c). Exam tip: decide signs from (2ab), (-2ac), and (-2bc).
Step 2
Why this answer is correct
The correct answer is D. ( (a+b-c)2 ). This is the perfect square of (a), (b), and (-c). Exam tip: decide signs from (2ab), (-2ac), and (-2bc).
Step 3
Exam Tip
यह (a), (b), (-c) का पूर्ण वर्ग है। परीक्षा में (2ab), (-2ac), (-2bc) से चिन्ह तय करें।
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\(x^4+2x^2y^2+y^4-16z^4\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^4+2x^2y^2+y^4-16z^4\)?
#compound square
#difference of squares
#factorisation
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A ( \(x^2+y^2-4z^2\)\(x^2+y^2+4z^2\) )
B ( (x+y-4z)(x+y+4z) )
C ( \(x^2-y^2-4z^2\)\(x^2-y^2+4z^2\) )
D ( \(x^2+y^2+4z^2\)2 )
Explanation opens after your attempt
Correct Answer
A. ( \(x^2+y^2-4z^2\)\(x^2+y^2+4z^2\) )
Step 1
Concept
First write \(x^4+2x^2y^2+y^4\) as (\(x^2+y^2\)2 ). Exam tip: treat larger expressions as one combined square.
Step 2
Why this answer is correct
The correct answer is A. ( \(x^2+y^2-4z^2\)\(x^2+y^2+4z^2\) ). First write \(x^4+2x^2y^2+y^4\) as (\(x^2+y^2\)2 ). Exam tip: treat larger expressions as one combined square.
Step 3
Exam Tip
पहले \(x^4+2x^2y^2+y^4\) को (\(x^2+y^2\)2 ) बनाएं। परीक्षा में बड़े पदों को एक संयुक्त वर्ग मानें।
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\(a^6-b^6\) का एक पूर्ण गुणनखंड रूप कौन सा है?
Which is one complete factorised form of \(a^6-b^6\)?
#sixth powers
#cube identities
#complete factorisation
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A ( \(a^3-b^3\)\(a^3+b^3\) )
B ( (a-b)(a+b)\(a^2+ab+b^2\)\(a^2-ab+b^2\) )
C ( (a-b)3 (a+b)3 )
D ( \(a^2-b^2\)3 )
Explanation opens after your attempt
Correct Answer
B. ( (a-b)(a+b)\(a^2+ab+b^2\)\(a^2-ab+b^2\) )
Step 1
Concept
\(a^6-b^6\) can be fully factored using both cube and square identities. Exam tip: factor both \(a^3-b^3\) and \(a^3+b^3\) further.
Step 2
Why this answer is correct
The correct answer is B. ( (a-b)(a+b)\(a^2+ab+b^2\)\(a^2-ab+b^2\) ). \(a^6-b^6\) can be fully factored using both cube and square identities. Exam tip: factor both \(a^3-b^3\) and \(a^3+b^3\) further.
Step 3
Exam Tip
\(a^6-b^6\) को घन और वर्ग दोनों पहचान से पूर्ण रूप में तोड़ा जा सकता है। परीक्षा में \(a^3-b^3\) और \(a^3+b^3\) दोनों को आगे तोड़ें।
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\(3x^2+2xy-8y^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(3x^2+2xy-8y^2\).
#quadratic in variables
#middle term
#factorisation
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A ( (3x-4y)(x+2y) )
B ( (3x+4y)(x-2y) )
C ( (3x-4y)(x+2y) )
D ( (x-4y)(3x+2y) )
Explanation opens after your attempt
Correct Answer
C. ( (3x-4y)(x+2y) )
Step 1
Concept
The split (6xy-4xy) gives (2xy). Exam tip: the signs are opposite because the last term is negative.
Step 2
Why this answer is correct
The correct answer is C. ( (3x-4y)(x+2y) ). The split (6xy-4xy) gives (2xy). Exam tip: the signs are opposite because the last term is negative.
Step 3
Exam Tip
(6xy-4xy) से (2xy) बनता है। परीक्षा में ऋणात्मक अंतिम पद के कारण चिन्ह विपरीत होंगे।
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\(10p^2-23pq+12q^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(10p^2-23pq+12q^2\)?
#quadratic in variables
#ac method
#factorisation
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A ( (5p-4q)(2p-3q) )
B ( (10p-3q)(p-4q) )
C ( (5p+4q)(2p+3q) )
D ( (5p-4q)(2p-3q) )
Explanation opens after your attempt
Correct Answer
D. ( (5p-4q)(2p-3q) )
Step 1
Concept
Expanding gives \(10p^2-15pq-8pq+12q^2\). Exam tip: check that (-15pq) and (-8pq) add to (-23pq).
Step 2
Why this answer is correct
The correct answer is D. ( (5p-4q)(2p-3q) ). Expanding gives \(10p^2-15pq-8pq+12q^2\). Exam tip: check that (-15pq) and (-8pq) add to (-23pq).
Step 3
Exam Tip
फैलाने पर \(10p^2-15pq-8pq+12q^2\) मिलता है। परीक्षा में (-15pq) और (-8pq) का योग (-23pq) जांचें।
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(x-3 +27y-3 -9xy(x+3y)) का गुणनखंड रूप क्या है?
What is the factorised form of (x-3 +27y-3 -9xy(x+3y))?
#sum of cubes
#perfect square
#factorisation
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A ( (x+3y)(x-3y)2 )
B ( (x-3y)(x+3y)2 )
C ( (x+3y)\(x^2-3xy+9y^2\) )
D ( (x-3y)\(x^2+3xy+9y^2\) )
Explanation opens after your attempt
Correct Answer
A. ( (x+3y)(x-3y)2 )
Step 1
Concept
The expression \(x^3+27y^3\) has factor ((x+3y)). The inside becomes \(x^2-12xy+9y^2\), giving ((x-3y)2 ).
Step 2
Why this answer is correct
The correct answer is A. ( (x+3y)(x-3y)2 ). The expression \(x^3+27y^3\) has factor ((x+3y)). The inside becomes \(x^2-12xy+9y^2\), giving ((x-3y)2 ).
Step 3
Exam Tip
\(x^3+27y^3\) में ((x+3y)) गुणनखंड आता है। अंदर \(x^2-12xy+9y^2\) बनकर ((x-3y)2 ) देता है।
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\(4a^2-4ab+b^2-25c^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(4a^2-4ab+b^2-25c^2\)?
#perfect square
#difference of squares
#factorisation
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A ( (2a+b-5c)(2a+b+5c) )
B ( (2a-b-5c)(2a-b+5c) )
C ( (4a-b-25c)(a+b+c) )
D ( (2a-b+5c)2 )
Explanation opens after your attempt
Correct Answer
B. ( (2a-b-5c)(2a-b+5c) )
Step 1
Concept
Write \(4a^2-4ab+b^2\) as ((2a-b)2 ). Exam tip: then use (25c-2 =(5c)2 ) for difference of squares.
Step 2
Why this answer is correct
The correct answer is B. ( (2a-b-5c)(2a-b+5c) ). Write \(4a^2-4ab+b^2\) as ((2a-b)2 ). Exam tip: then use (25c-2 =(5c)2 ) for difference of squares.
Step 3
Exam Tip
\(4a^2-4ab+b^2\) को ((2a-b)2 ) लिखें। परीक्षा में फिर (25c-2 =(5c)2 ) लगाकर अंतर वर्ग करें।
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\(9x^4-30x^2+25\) का गुणनखंड रूप क्या है?
What is the factorised form of \(9x^4-30x^2+25\)?
#perfect square
#biquadratic
#factorisation
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A ( \(3x^2+5\)2 )
B ( \(9x^2-5\)2 )
C ( \(3x^2-5\)2 )
D ( (3x-5)(3x+5) )
Explanation opens after your attempt
Correct Answer
C. ( \(3x^2-5\)2 )
Step 1
Concept
It is (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ). Exam tip: identify perfect squares involving \(x^4\) too.
Step 2
Why this answer is correct
The correct answer is C. ( \(3x^2-5\)2 ). It is (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ). Exam tip: identify perfect squares involving \(x^4\) too.
Step 3
Exam Tip
यह (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ) है। परीक्षा में \(x^4\) वाले पूर्ण वर्ग को भी पहचानें।
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\(x^2+6x+9-4y^2+12y-9\) का सरल गुणनखंड रूप चुनिए।
Choose the simplified factorised form of \(x^2+6x+9-4y^2+12y-9\).
#difference of squares
#completion
#simplification
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A ( (x+3-2y+3)(x+3+2y-3) )
B ( (x-2y+6)(x+2y) )
C ( (x+2y+6)(x-2y) )
D ( (x+3)2 -(2y-3)2 )
Explanation opens after your attempt
Correct Answer
B. ( (x-2y+6)(x+2y) )
Step 1
Concept
Writing it as ((x+3)2 -(2y-3)2 ) gives the simplified form ((x-2y+6)(x+2y)). Exam tip: simplify the final answer.
Step 2
Why this answer is correct
The correct answer is B. ( (x-2y+6)(x+2y) ). Writing it as ((x+3)2 -(2y-3)2 ) gives the simplified form ((x-2y+6)(x+2y)). Exam tip: simplify the final answer.
Step 3
Exam Tip
इसे ((x+3)2 -(2y-3)2 ) लिखने पर सरल रूप ((x-2y+6)(x+2y)) आता है। परीक्षा में अंतिम उत्तर को सरल करें।
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\(2x^2+5xy-12y^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(2x^2+5xy-12y^2\)?
#quadratic in variables
#ac method
#factorisation
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A ( (2x-3y)(x+4y) )
B ( (2x+3y)(x-4y) )
C ( (x+3y)(2x-4y) )
D ( (2x-3y)(x+4y) )
Explanation opens after your attempt
Correct Answer
D. ( (2x-3y)(x+4y) )
Step 1
Concept
The split (8xy-3xy) gives (5xy), and the product is \(-24x^2y^2\). Exam tip: split the middle term using the (ac) method.
Step 2
Why this answer is correct
The correct answer is D. ( (2x-3y)(x+4y) ). The split (8xy-3xy) gives (5xy), and the product is \(-24x^2y^2\). Exam tip: split the middle term using the (ac) method.
Step 3
Exam Tip
(8xy-3xy) से (5xy) बनता है और गुणनफल \(-24x^2y^2\) है। परीक्षा में (ac) विधि से मध्य पद तोड़ें।
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\(x^4+4y^4+4x^2y^2-z^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^4+4y^4+4x^2y^2-z^2\)?
#compound square
#difference of squares
#factorisation
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A ( \(x^2+2y^2-z\)\(x^2+2y^2+z\) )
B ( \(x^2-2y^2-z\)\(x^2-2y^2+z\) )
C ( (x+2y-z)(x+2y+z) )
D ( \(x^2+2y^2+z\)2 )
Explanation opens after your attempt
Correct Answer
A. ( \(x^2+2y^2-z\)\(x^2+2y^2+z\) )
Step 1
Concept
First write \(x^4+4x^2y^2+4y^4\) as (\(x^2+2y^2\)2 ). Exam tip: arranging the terms correctly helps.
Step 2
Why this answer is correct
The correct answer is A. ( \(x^2+2y^2-z\)\(x^2+2y^2+z\) ). First write \(x^4+4x^2y^2+4y^4\) as (\(x^2+2y^2\)2 ). Exam tip: arranging the terms correctly helps.
Step 3
Exam Tip
पहले \(x^4+4x^2y^2+4y^4\) को (\(x^2+2y^2\)2 ) बनाएं। परीक्षा में पदों को सही क्रम में लगाना मदद करता है।
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\(a^4+2a^2b^2+b^4-c^4\) का पूर्ण गुणनखंड रूप चुनिए।
Choose the complete factorised form of \(a^4+2a^2b^2+b^4-c^4\).
#fourth powers
#difference of squares
#factorisation
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A ( \(a^2+b^2-c^2\)\(a^2+b^2+c^2\) )
B ( (a+b-c)(a+b+c) )
C ( \(a^2-b^2-c^2\)\(a^2-b^2+c^2\) )
D ( \(a^2+b^2+c^2\)2 )
Explanation opens after your attempt
Correct Answer
A. ( \(a^2+b^2-c^2\)\(a^2+b^2+c^2\) )
Step 1
Concept
Write \(a^4+2a^2b^2+b^4\) as (\(a^2+b^2\)2 ). Exam tip: recognise (c-4 =\(c^2\)2 ).
Step 2
Why this answer is correct
The correct answer is A. ( \(a^2+b^2-c^2\)\(a^2+b^2+c^2\) ). Write \(a^4+2a^2b^2+b^4\) as (\(a^2+b^2\)2 ). Exam tip: recognise (c-4 =\(c^2\)2 ).
Step 3
Exam Tip
\(a^4+2a^2b^2+b^4\) को (\(a^2+b^2\)2 ) लिखें। परीक्षा में (c-4 =\(c^2\)2 ) पहचानें।
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\(27x^3-64y^3\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(27x^3-64y^3\)?
#difference of cubes
#identity
#factorisation
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A ( (3x+4y)\(9x^2-12xy+16y^2\) )
B ( (3x-4y)\(9x^2+12xy+16y^2\) )
C ( (3x-4y)\(9x^2-12xy+16y^2\) )
D ( (27x-64y)\(x^2+xy+y^2\) )
Explanation opens after your attempt
Correct Answer
B. ( (3x-4y)\(9x^2+12xy+16y^2\) )
Step 1
Concept
It is ((3x)3 -(4y)3 ). Exam tip: in difference of cubes, the second bracket is \(a^2+ab+b^2\).
Step 2
Why this answer is correct
The correct answer is B. ( (3x-4y)\(9x^2+12xy+16y^2\) ). It is ((3x)3 -(4y)3 ). Exam tip: in difference of cubes, the second bracket is \(a^2+ab+b^2\).
Step 3
Exam Tip
यह ((3x)3 -(4y)3 ) है। परीक्षा में घनों के अंतर में दूसरा ब्रैकेट \(a^2+ab+b^2\) होता है।
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\(125m^3+216n^3\) का गुणनखंड रूप क्या है?
What is the factorised form of \(125m^3+216n^3\)?
#sum of cubes
#identity
#factorisation
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A ( (5m-6n)\(25m^2+30mn+36n^2\) )
B ( (5m+6n)\(25m^2+30mn+36n^2\) )
C ( (5m+6n)\(25m^2-30mn+36n^2\) )
D ( (125m+216n)\(m^2-mn+n^2\) )
Explanation opens after your attempt
Correct Answer
C. ( (5m+6n)\(25m^2-30mn+36n^2\) )
Step 1
Concept
It is ((5m)3 +(6n)3 ). Exam tip: in sum of cubes, the middle term of the second bracket is negative.
Step 2
Why this answer is correct
The correct answer is C. ( (5m+6n)\(25m^2-30mn+36n^2\) ). It is ((5m)3 +(6n)3 ). Exam tip: in sum of cubes, the middle term of the second bracket is negative.
Step 3
Exam Tip
यह ((5m)3 +(6n)3 ) है। परीक्षा में घनों के योग में दूसरे ब्रैकेट का मध्य पद ऋणात्मक होता है।
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\(6x^2+11xy-10y^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(6x^2+11xy-10y^2\).
#quadratic in variables
#signs
#factorisation
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A ( (3x-2y)(2x+5y) )
B ( (6x-5y)(x+2y) )
C ( (3x+2y)(2x-5y) )
D ( (3x-2y)(2x+5y) )
Explanation opens after your attempt
Correct Answer
D. ( (3x-2y)(2x+5y) )
Step 1
Concept
The split (15xy-4xy) gives (11xy). Exam tip: when the last term is negative, look for opposite signs.
Step 2
Why this answer is correct
The correct answer is D. ( (3x-2y)(2x+5y) ). The split (15xy-4xy) gives (11xy). Exam tip: when the last term is negative, look for opposite signs.
Step 3
Exam Tip
(15xy-4xy) से (11xy) बनता है। परीक्षा में अंतिम पद ऋणात्मक हो तो विपरीत चिन्हों की जोड़ी खोजें।
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\(x^2-4y^2+2x+1\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-4y^2+2x+1\).
#completion
#difference of squares
#factorisation
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A ( (x+1-2y)(x+1+2y) )
B ( (x-1-2y)(x-1+2y) )
C ( (x+2y+1)2 )
D ( (x+1-4y)(x+1+y) )
Explanation opens after your attempt
Correct Answer
A. ( (x+1-2y)(x+1+2y) )
Step 1
Concept
Write \(x^2+2x+1\) as ((x+1)2 ). Exam tip: treat the remaining \(-4y^2\) as (-(2y)2 ).
Step 2
Why this answer is correct
The correct answer is A. ( (x+1-2y)(x+1+2y) ). Write \(x^2+2x+1\) as ((x+1)2 ). Exam tip: treat the remaining \(-4y^2\) as (-(2y)2 ).
Step 3
Exam Tip
\(x^2+2x+1\) को ((x+1)2 ) लिखें। परीक्षा में बाकी \(-4y^2\) को (-(2y)2 ) समझें।
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\(49a^2-70ab+25b^2-c^2\) का सही गुणनखंड क्या है?
What is the correct factorisation of \(49a^2-70ab+25b^2-c^2\)?
#perfect square
#difference of squares
#factorisation
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A ( (7a+5b-c)(7a+5b+c) )
B ( (7a-5b-c)(7a-5b+c) )
C ( (49a-25b-c)(a+b+c) )
D ( (7a-5b+c)2 )
Explanation opens after your attempt
Correct Answer
B. ( (7a-5b-c)(7a-5b+c) )
Step 1
Concept
First write \(49a^2-70ab+25b^2\) as ((7a-5b)2 ). Exam tip: then apply difference of squares with \(c^2\).
Step 2
Why this answer is correct
The correct answer is B. ( (7a-5b-c)(7a-5b+c) ). First write \(49a^2-70ab+25b^2\) as ((7a-5b)2 ). Exam tip: then apply difference of squares with \(c^2\).
Step 3
Exam Tip
पहले \(49a^2-70ab+25b^2\) को ((7a-5b)2 ) बनाएं। परीक्षा में फिर \(c^2\) के साथ अंतर वर्ग लगाएं।
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\(x^4-2x^2y^2+y^4-z^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(x^4-2x^2y^2+y^4-z^2\)?
#compound square
#difference of squares
#factorisation
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A ( \(x^2+y^2-z\)\(x^2+y^2+z\) )
B ( (x-y-z)(x-y+z) )
C ( \(x^2-y^2-z\)\(x^2-y^2+z\) )
D ( \(x^2-y^2+z\)2 )
Explanation opens after your attempt
Correct Answer
C. ( \(x^2-y^2-z\)\(x^2-y^2+z\) )
Step 1
Concept
First write \(x^4-2x^2y^2+y^4\) as (\(x^2-y^2\)2 ). Exam tip: treat the compound part as one unit.
Step 2
Why this answer is correct
The correct answer is C. ( \(x^2-y^2-z\)\(x^2-y^2+z\) ). First write \(x^4-2x^2y^2+y^4\) as (\(x^2-y^2\)2 ). Exam tip: treat the compound part as one unit.
Step 3
Exam Tip
पहले \(x^4-2x^2y^2+y^4\) को (\(x^2-y^2\)2 ) लिखें। परीक्षा में संयुक्त पद को एक इकाई की तरह लें।
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\(a^2-b^2+2bc-c^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(a^2-b^2+2bc-c^2\)?
#difference of squares
#completion
#factorisation
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A ( (a-b+c)(a+b-c) )
B ( (a+b+c)(a-b-c) )
C ( (a-b-c)(a+b+c) )
D ( (a+b-c)2 )
Explanation opens after your attempt
Correct Answer
A. ( (a-b+c)(a+b-c) )
Step 1
Concept
Write \(-b^2+2bc-c^2\) as (-(b-c)2 ). Then apply difference of squares to (a-2 -(b-c)2 ).
Step 2
Why this answer is correct
The correct answer is A. ( (a-b+c)(a+b-c) ). Write \(-b^2+2bc-c^2\) as (-(b-c)2 ). Then apply difference of squares to (a-2 -(b-c)2 ).
Step 3
Exam Tip
\(-b^2+2bc-c^2\) को (-(b-c)2 ) लिखें। तब (a-2 -(b-c)2 ) पर अंतर वर्ग लगाएं।
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