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555-605 (Medium)|   Algebra|      
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Bunuel
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(2uv)^2 + (u^2 - v^2)^2 = 19 Jun 2020, 06:15
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E
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25% (medium)

Question Stats:

75% (01:27) correct 25% (02:08) wrong based on 112 sessions

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\((2uv)^2 + (u^2 - v^2)^2 = \)


A. \(2uv\)

B. \(u^2-v^2\)

C. \(u^2+v^2\)

D. \((2uv)^2 + (u^2+v^2)^2\)

E. \((u^2+v^2)^2\)
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E
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(2uv)^2 + (u^2 - v^2)^2 = 19 Jun 2020, 06:21
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(2uv)^2 + (u^2 - v^2)^2 = X
4u^2v^2 + u^4 + v^4 -2u^2v^2 = X
u^4 + v^4 + 2u^2v^2 = X
(U^2 + V^2)^2 = X

Answer is E

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(2uv)^2 + (u^2 - v^2)^2 = 19 Jun 2020, 06:21
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Bunuel
\((2uv)^2 + (u^2 - v^2)^2 = \)


A. \(2uv\)

B. \(u^2-v^2\)

C. \(u^2+v^2\)

D. \((2uv)^2 + (u^2+v^2)^2\)

E. \((u^2+v^2)^2\)
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\((2uv)^2 + (u^2 - v^2)^2 = 4*u^2*v^2 + u^4 + v^4 - 2*u^2*v^2 = 2*u^2*v^2 + u^4 + v^4 = (u^2+v^2)^2\)

Answer: Option E
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(2uv)^2 + (u^2 - v^2)^2 = 19 Jun 2020, 06:23
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Bunuel
\((2uv)^2 + (u^2 - v^2)^2 = \)


A. \(2uv\)

B. \(u^2-v^2\)

C. \(u^2+v^2\)

D. \((2uv)^2 + (u^2+v^2)^2\)

E. \((u^2+v^2)^2\)
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Take: \((2uv)^2 + (u^2 - v^2)^2 \)

Expand to get: \(4u^2v^2 + [u^4 - 2u^2v^2 + v^4] \)

Simplify: \(u^4 + 2u^2v^2 + v^4 \)

Factor: \((u^2+v^2)^2\)

Answer: E

Cheers,
Brent
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(2uv)^2 + (u^2 - v^2)^2 = 20 Jun 2020, 01:21
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Bunuel
\((2uv)^2 + (u^2 - v^2)^2 = \)


A. \(2uv\)

B. \(u^2-v^2\)

C. \(u^2+v^2\)

D. \((2uv)^2 + (u^2+v^2)^2\)

E. \((u^2+v^2)^2\)
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if its too much algebra for you then let u=1 and v=1
(2*1)^2 + (1-1)^2 = 4
put u=1 and v=1 in all answer choices and only E gives out 4.
Hence, E.
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(2uv)^2 + (u^2 - v^2)^2 = 16 Apr 2025, 08:48
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