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

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Math Expert
Joined: 02 Sep 2009
Posts: 46129
Which of the following is equivalent to xy + 2xy(1 + y)2y? [#permalink]

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15 Jan 2018, 06:24
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Difficulty:

35% (medium)

Question Stats:

74% (01:20) correct 26% (01:37) wrong based on 42 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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15 Jan 2018, 06:35
Expanding we get,
=xy+4xy^2 +4xy^3
=xy(1+4y+4y^2)
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Re: Which of the following is equivalent to xy + 2xy(1 + y)2y? [#permalink]

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15 Jan 2018, 08:18
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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Math Expert
Joined: 02 Aug 2009
Posts: 5887
Re: Which of the following is equivalent to xy + 2xy(1 + y)2y? [#permalink]

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15 Jan 2018, 08:31
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?   [#permalink] 15 Jan 2018, 08:31
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