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Which of the following is equivalent to xy + 2xy(1 + y)2y?

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Which of the following is equivalent to xy + 2xy(1 + y)2y?  [#permalink]

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New post 15 Jan 2018, 05:24
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A
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C
D
E

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Question Stats:

76% (01:42) correct 24% (02:13) wrong based on 58 sessions

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Which of the following is equivalent to \(xy + 2xy(1 + y)2y\)?


(A) \(xy(2y + 1)^2\)

(B) \((2xy + 1)(2xy - 1)\)

(C) \((2x + y)^2\)

(D) \((x + 2y)^2\)

(E) \(y(x - 2y)^2\)

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Re: Which of the following is equivalent to xy + 2xy(1 + y)2y?  [#permalink]

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Re: Which of the following is equivalent to xy + 2xy(1 + y)2y?  [#permalink]

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New post 15 Jan 2018, 07:18
Bunuel wrote:
Which of the following is equivalent to \(xy + 2xy(1 + y)2y\)?

(A) xy(2y + 1)^2
(B) (2xy + 1)(2xy - 1)
(C) (2x + y)^2
(D) (x + 2y)^2
(E) y(x - 2y)^2



\(xy + 2xy(1 + y)2y\)

Taking xy common, we get

\(xy(1 + 4y(1+y)) = xy(1 + 4y + 4y^2) = xy(2y+1)^2\) (Option A)

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Re: Which of the following is equivalent to xy + 2xy(1 + y)2y?  [#permalink]

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New post 15 Jan 2018, 07:31
Bunuel wrote:
Which of the following is equivalent to \(xy + 2xy(1 + y)2y\)?

(A) xy(2y + 1)^2
(B) (2xy + 1)(2xy - 1)
(C) (2x + y)^2
(D) (x + 2y)^2
(E) y(x - 2y)^2


Substitution again is best bet here, but yes smart number..
put y as 0..
\(xy + 2xy(1 + y)2y=0\)
see choices..
(A) xy(2y + 1)^2 ....0...yes
(B) (2xy + 1)(2xy - 1)....(0-1)(0+1)=-1...NO
(C) (2x + y)^2 ......(2x)^2....NO
(D) (x + 2y)^2 ......x^2.....NO
(E) y(x - 2y)^2.....0...yes..

Now lets choose between A and E..
take x as 0
\(xy + 2xy(1 + y)2y=0\)
(A) xy(2y + 1)^2 ......0...YES
(E) y(x - 2y)^2.......y*4y^2.....NO

ans A
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Re: Which of the following is equivalent to xy + 2xy(1 + y)2y? &nbs [#permalink] 15 Jan 2018, 07:31
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