difference of squares se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
75 questions tagged with difference of squares.
If (p(x)=x-2-49), which value is correct for (p(a)=0)?
C. (a=7)
(p(7)=49-49=0). The zeros of \(x^2-49\) are (7) and (-7).
The correct answer is C. (a=7). (p(7)=49-49=0). The zeros of \(x^2-49\) are (7) and (-7).
(p(7)=49-49=0)। \(x^2-49\) के शून्य (7) और (-7) हैं।
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If (p(x)=x-2-25), which value is correct for (p(a)=0)?
C. (a=5)
(p(5)=25-25=0). The zeros of \(x^2-25\) are (5) and (-5).
The correct answer is C. (a=5). (p(5)=25-25=0). The zeros of \(x^2-25\) are (5) and (-5).
(p(5)=25-25=0)। \(x^2-25\) के शून्य (5) और (-5) हैं।
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If (p(x)=x-2-9), which value of (a) is correct for (p(a)=0)?
C. (a=3)
(p(3)=9-9=0). The zeros of \(x^2-9\) are (3) and (-3).
The correct answer is C. (a=3). (p(3)=9-9=0). The zeros of \(x^2-9\) are (3) and (-3).
(p(3)=9-9=0)। \(x^2-9\) के शून्य (3) और (-3) हैं।
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What is the simplified form of \(\frac{x^{10}-1024}{x^{5}-32}\), where \(x^{5}\neq32\)?
B. \(x^{5}+32\)
We use (x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\)). Cancelling the common factor leaves \(x^{5}+32\).
The correct answer is B. \(x^{5}+32\). We use (x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\)). Cancelling the common factor leaves \(x^{5}+32\).
(x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\))। समान गुणनखंड कटने पर \(x^{5}+32\) बचता है।
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What is the simplified form of \(\frac{x^{6}-64}{x^{3}-8}\), where \(x^{3}\neq8\)?
B. \(x^{3}+8\)
We use (x^{6}-64=\(x^{3}\)^{2}-8^{2}=\(x^{3}-8\)\(x^{3}+8\)). Cancelling the common factor leaves \(x^{3}+8\).
The correct answer is B. \(x^{3}+8\). We use (x^{6}-64=\(x^{3}\)^{2}-8^{2}=\(x^{3}-8\)\(x^{3}+8\)). Cancelling the common factor leaves \(x^{3}+8\).
(x^{6}-64=\(x^{3}\)^{2}-8^{2}=\(x^{3}-8\)\(x^{3}+8\))। समान गुणनखंड कटने पर \(x^{3}+8\) बचता है।
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If \(x^2+9 \neq 0\), what is the simplified form of \(\dfrac{x^4-81}{x^2+9}\)?
A. \(,x^2-9,\)
(x-4-81=\(x^2-9\)\(x^2+9\)), so the simplified form is \(x^2-9\). In exams, treat \(x^4\) as (\(x^2\)2) while factoring.
The correct answer is A. \(,x^2-9,\). (x-4-81=\(x^2-9\)\(x^2+9\)), so the simplified form is \(x^2-9\). In exams, treat \(x^4\) as (\(x^2\)2) while factoring.
(x-4-81=\(x^2-9\)\(x^2+9\)), इसलिए सरल रूप \(x^2-9\) है। परीक्षा में \(x^4\) को (\(x^2\)2) मानकर factor करें।
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If \(x+y \neq 0\), what is the simplified form of \(\dfrac{x^2-y^2}{x+y}\)?
A. (,x-y,)
Because (x-2-y-2=(x-y)(x+y)), ((x+y)) cancels and (x-y) remains. In exams, identify difference of squares quickly.
The correct answer is A. (,x-y,). Because (x-2-y-2=(x-y)(x+y)), ((x+y)) cancels and (x-y) remains. In exams, identify difference of squares quickly.
क्योंकि (x-2-y-2=(x-y)(x+y)), इसलिए ((x+y)) कटकर (x-y) बचता है। परीक्षा में difference of squares तुरंत पहचानें।
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If \(x^2 \neq 4\), what is the simplified form of \(\dfrac{x^4-16}{x^2-4}\)?
A. \(,x^2+4,\)
(x-4-16=\(x^2-4\)\(x^2+4\)), so the simplified form is \(x^2+4\). In exams, treat \(x^4\) as (\(x^2\)2) for factorisation.
The correct answer is A. \(,x^2+4,\). (x-4-16=\(x^2-4\)\(x^2+4\)), so the simplified form is \(x^2+4\). In exams, treat \(x^4\) as (\(x^2\)2) for factorisation.
(x-4-16=\(x^2-4\)\(x^2+4\)), इसलिए सरल रूप \(x^2+4\) है। परीक्षा में \(x^4\) को (\(x^2\)2) समझकर factor करें।
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What is the factorized form of \(100x^2-121y^2\)?
A. ((10x-11y)(10x+11y))
(100x-2-121y-2=(10x)2-(11y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).
The correct answer is A. ((10x-11y)(10x+11y)). (100x-2-121y-2=(10x)2-(11y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).
(100x-2-121y-2=(10x)2-(11y)2) है। अंतर के वर्ग का नियम (\(a^2-b^2\)=(a-b)(a+b)) लगाएँ।
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What is the simplified form of ((7x+6)(7x-6))?
A. \(49x^2-36\)
((a+b)(a-b)=a-2-b-2). Here (a=7x) and (b=6).
The correct answer is A. \(49x^2-36\). ((a+b)(a-b)=a-2-b-2). Here (a=7x) and (b=6).
((a+b)(a-b)=a-2-b-2) है। यहाँ (a=7x) और (b=6) हैं।
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What is the value of \(3.5^2-2.5^2\)?
B. (6)
Using (a-2-b-2=(a-b)(a+b)), ((3.5-2.5)(3.5+2.5)=1\cdot6=6). Identities also work with decimals.
The correct answer is B. (6). Using (a-2-b-2=(a-b)(a+b)), ((3.5-2.5)(3.5+2.5)=1\cdot6=6). Identities also work with decimals.
(a-2-b-2=(a-b)(a+b)) से ((3.5-2.5)(3.5+2.5)=1\cdot6=6)। पहचान दशमलव में भी लागू होती है।
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What is the factorized form of \(121x^2-144\)?
A. ((11x-12)(11x+12))
(121x-2-144=(11x)2-122). Apply the difference of squares identity.
The correct answer is A. ((11x-12)(11x+12)). (121x-2-144=(11x)2-122). Apply the difference of squares identity.
(121x-2-144=(11x)2-122) है। अंतर के वर्ग का नियम लगाएँ।
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What is the simplified form of ((x+12)(x-12))?
A. \(x^2-144\)
This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+12)(x-12)=x-2-144).
The correct answer is A. \(x^2-144\). This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+12)(x-12)=x-2-144).
यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए ((x+12)(x-12)=x-2-144) है।
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What is the factorized form of \(81x^2-100y^2\)?
A. ((9x-10y)(9x+10y))
(81x-2-100y-2=(9x)2-(10y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).
The correct answer is A. ((9x-10y)(9x+10y)). (81x-2-100y-2=(9x)2-(10y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).
(81x-2-100y-2=(9x)2-(10y)2) है। अंतर के वर्ग का नियम (\(a^2-b^2\)=(a-b)(a+b)) लगाएँ।
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What is the simplified form of ((6x+5)(6x-5))?
A. \(36x^2-25\)
((a+b)(a-b)=a-2-b-2). Here (a=6x) and (b=5).
The correct answer is A. \(36x^2-25\). ((a+b)(a-b)=a-2-b-2). Here (a=6x) and (b=5).
((a+b)(a-b)=a-2-b-2) है। यहाँ (a=6x) और (b=5) हैं।
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What is the value of \(2.5^2-1.5^2\)?
C. (4)
Using (a-2-b-2=(a-b)(a+b)), ((2.5-1.5)(2.5+1.5)=1\cdot4=4). Identities also work with decimals.
The correct answer is C. (4). Using (a-2-b-2=(a-b)(a+b)), ((2.5-1.5)(2.5+1.5)=1\cdot4=4). Identities also work with decimals.
(a-2-b-2=(a-b)(a+b)) से ((2.5-1.5)(2.5+1.5)=1\cdot4=4)। पहचान दशमलव में भी लागू होती है।
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What is the factorized form of \(64x^2-81\)?
A. ((8x-9)(8x+9))
(64x-2-81=(8x)2-92). Apply the difference of squares identity.
The correct answer is A. ((8x-9)(8x+9)). (64x-2-81=(8x)2-92). Apply the difference of squares identity.
(64x-2-81=(8x)2-92) है। अंतर के वर्ग का नियम लगाएँ।
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What is the simplified form of ((x+9)(x-9))?
A. \(x^2-81\)
This is of the form ((a+b)(a-b)=a-2-b-2). Therefore the answer is \(x^2-81\).
The correct answer is A. \(x^2-81\). This is of the form ((a+b)(a-b)=a-2-b-2). Therefore the answer is \(x^2-81\).
यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए उत्तर \(x^2-81\) है।
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What is the simplified form of ((5x+4)(5x-4))?
A. \(25x^2-16\)
((a+b)(a-b)=a-2-b-2). Here (a=5x) and (b=4).
The correct answer is A. \(25x^2-16\). ((a+b)(a-b)=a-2-b-2). Here (a=5x) and (b=4).
((a+b)(a-b)=a-2-b-2) है। यहाँ (a=5x) और (b=4) हैं।
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What is the value of \(1.5^2-0.5^2\)?
B. (2)
Using (a-2-b-2=(a-b)(a+b)), ((1.5-0.5)(1.5+0.5)=1\cdot2=2). Identities also work with decimals.
The correct answer is B. (2). Using (a-2-b-2=(a-b)(a+b)), ((1.5-0.5)(1.5+0.5)=1\cdot2=2). Identities also work with decimals.
(a-2-b-2=(a-b)(a+b)) से ((1.5-0.5)(1.5+0.5)=1\cdot2=2)। पहचान दशमलव में भी लागू होती है।
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What is the factorized form of \(49x^2-64\)?
A. ((7x-8)(7x+8))
(49x-2-64=(7x)2-82). Apply the difference of squares identity.
The correct answer is A. ((7x-8)(7x+8)). (49x-2-64=(7x)2-82). Apply the difference of squares identity.
(49x-2-64=(7x)2-82) है। अंतर के वर्ग का नियम लगाएँ।
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What is the simplified form of ((x+7)(x-7))?
A. \(x^2-49\)
This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+7)(x-7)=x-2-49).
The correct answer is A. \(x^2-49\). This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+7)(x-7)=x-2-49).
यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए ((x+7)(x-7)=x-2-49) है।
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C. (12)
The equation is ((x-5)(x+5)=119). Thus \(x^2-25=119\), giving (x=12).
The correct answer is C. (12). The equation is ((x-5)(x+5)=119). Thus \(x^2-25=119\), giving (x=12).
समीकरण ((x-5)(x+5)=119) है। इससे \(x^2-25=119\) और (x=12) मिलता है।
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B. (40) वर्ष(40) years
((x+10)(x-10)=1500) gives \(x^2-100=1500\), so (x=40). The difference of squares idea helps in such questions.
The correct answer is B. (40) वर्ष / (40) years. ((x+10)(x-10)=1500) gives \(x^2-100=1500\), so (x=40). The difference of squares idea helps in such questions.
((x+10)(x-10)=1500) से \(x^2-100=1500\), इसलिए (x=40) है। ऐसे प्रश्न में अंतर के वर्ग का सूत्र मदद करता है।
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B. (48) वर्ष(48) years
((x+12)(x-12)=2160) gives \(x^2-144=2160\), so (x=48). Always take age as positive.
The correct answer is B. (48) वर्ष / (48) years. ((x+12)(x-12)=2160) gives \(x^2-144=2160\), so (x=48). Always take age as positive.
((x+12)(x-12)=2160) से \(x^2-144=2160\), इसलिए (x=48) है। आयु हमेशा धनात्मक लें।
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B. (37) वर्ष(37) years
((x+6)(x-6)=1333) gives \(x^2-36=1333\) and (x=37). The difference of squares idea helps in such questions.
The correct answer is B. (37) वर्ष / (37) years. ((x+6)(x-6)=1333) gives \(x^2-36=1333\) and (x=37). The difference of squares idea helps in such questions.
((x+6)(x-6)=1333) से \(x^2-36=1333\) और (x=37) है। ऐसे प्रश्न में अंतर के वर्ग का सूत्र मदद करता है।
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B. (40) वर्ष(40) years
((x+7)(x-7)=1675) gives \(x^2-49=1675\), so (x=40). Always take age as positive.
The correct answer is B. (40) वर्ष / (40) years. ((x+7)(x-7)=1675) gives \(x^2-49=1675\), so (x=40). Always take age as positive.
((x+7)(x-7)=1675) से \(x^2-49=1675\), इसलिए (x=40) है। आयु हमेशा धनात्मक लें।
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B. (25) वर्ष(25) years
((x+4)(x-4)=609) gives \(x^2-16=609\) and (x=25). The difference of squares idea helps in such questions.
The correct answer is B. (25) वर्ष / (25) years. ((x+4)(x-4)=609) gives \(x^2-16=609\) and (x=25). The difference of squares idea helps in such questions.
((x+4)(x-4)=609) से \(x^2-16=609\) और (x=25) है। ऐसे प्रश्न में अंतर के वर्ग का सूत्र मदद करता है।
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B. (30) वर्ष(30) years
((x+5)(x-5)=875) gives \(x^2-25=875\), so (x=30). Always take age as positive.
The correct answer is B. (30) वर्ष / (30) years. ((x+5)(x-5)=875) gives \(x^2-25=875\), so (x=30). Always take age as positive.
((x+5)(x-5)=875) से \(x^2-25=875\), इसलिए (x=30) है। आयु हमेशा धनात्मक लें।
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If \(x^2-2ux+u^2-v^2=0\), what are its roots?
A. (x=u+v,u-v)
It is ((x-u)2-v-2=0), so \(x-u=\pm v\) and \(x=u\pm v\). In exams, quickly recognize the difference of squares.
The correct answer is A. (x=u+v,u-v). It is ((x-u)2-v-2=0), so \(x-u=\pm v\) and \(x=u\pm v\). In exams, quickly recognize the difference of squares.
यह ((x-u)2-v-2=0) है, इसलिए \(x-u=\pm v\) और \(x=u\pm v\) हैं। परीक्षा में वर्गों के अंतर को जल्दी पहचानें।
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