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(x + y)^2 – (x^2 – y^2 ) =
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22 Jul 2019, 02:38
22 Jul 2019, 02:38
Expert Reply
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Question Stats:
78% (00:51) correct
21% (00:54) wrong based on 149 sessions
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\((x + y)^2 – (x^2 – y^2 ) =\)
(A) \((x – y)^2\)
(B) \(2y^2\)
(C) \(2xy\)
(D) \(2x(y – x)\)
(E) \(2y(x + y)\)
(A) \((x – y)^2\)
(B) \(2y^2\)
(C) \(2xy\)
(D) \(2x(y – x)\)
(E) \(2y(x + y)\)
Re: (x + y)^2 – (x^2 – y^2 ) =
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22 Jul 2019, 10:56
22 Jul 2019, 10:56
1
This problem can be solved using the "difference of two squares" identity:
\((x^2 - y^2) = (x + y)(x - y)\)
\((x + y)^2 – (x^2 – y^2 )\)
\((x + y)^2 – (x + y)(x - y)\)
We can now factor out an (x + y):
\((x + y)[(x + y) - (x - y)]\)
\((x + y)(x + y - x + y)\)
\((x + y)(2y)\)
This is answer choice E.
\((x^2 - y^2) = (x + y)(x - y)\)
\((x + y)^2 – (x^2 – y^2 )\)
\((x + y)^2 – (x + y)(x - y)\)
We can now factor out an (x + y):
\((x + y)[(x + y) - (x - y)]\)
\((x + y)(x + y - x + y)\)
\((x + y)(2y)\)
This is answer choice E.
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Re: (x + y)^2 – (x^2 – y^2 ) =
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24 Jul 2019, 09:01
24 Jul 2019, 09:01
1
Carcass wrote:
\((x + y)^2 – (x^2 – y^2 ) =\)
(A) \((x – y)^2\)
(B) \(2y^2\)
(C) \(2xy\)
(D) \(2x(y – x)\)
(E) \(2y(x + y)\)
(A) \((x – y)^2\)
(B) \(2y^2\)
(C) \(2xy\)
(D) \(2x(y – x)\)
(E) \(2y(x + y)\)
Here's another approach....
GIVEN: (x + y)² – (x² – y²)
Rewrite as: (x + y)² – x² + y²
Expand first part as: x² + 2xy + y² – x² + y²
Simplify to get: 2xy + 2y²
Check the answer choices.... not there! We need to rewrite 2xy + 2y²
Take: 2xy + 2y²
Factor out 2y to get: 2y(x + y)
Answer: E
Cheers,
Brent
