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# (2 + x)(2 + y) – (2 + x) – (2 + y) =

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Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139604 [0], given: 12794

(2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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31 May 2017, 00:40
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Difficulty:

5% (low)

Question Stats:

98% (00:51) correct 2% (00:56) wrong based on 56 sessions

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$$(2 + x)(2 + y) – (2 + x) – (2 + y) =$$

(A) 2y
(B) xy
(C) x + y
(D) x – y
(E) x + y + xy
[Reveal] Spoiler: OA

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Kudos [?]: 139604 [0], given: 12794

DS Forum Moderator
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Re: (2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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31 May 2017, 03:14
(2+x)(2+y) = 4 + 2x + 2y + xy

Thus, (2+x)(2+y)–(2+x)–(2+y) = 4 + 2x + 2y + xy - 2 -x -2 - y = (x + y + xy)

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BSchool Forum Moderator
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Re: (2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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31 May 2017, 06:21
We need to find out the value of this expression
(2+x)(2+y)–(2+x)–(2+y)
Substituting values x=y=1

We get 9 - 3 - 3 = 3

Of the available answer options, only Option E gives us the same value as the expression.
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Target Test Prep Representative
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Re: (2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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01 Jun 2017, 16:28
Bunuel wrote:
$$(2 + x)(2 + y) – (2 + x) – (2 + y) =$$

(A) 2y
(B) xy
(C) x + y
(D) x – y
(E) x + y + xy

Let’s simplify the given expression:

(2 + x)(2 + y) - (2 + x) - (2 + y)

4 + 2x + 2y + yx - 2 - x - 2 - y

x + y + yx

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Kudos [?]: 1087 [0], given: 4

Manager
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Kudos [?]: 54 [0], given: 142

Re: (2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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17 Jul 2017, 09:44
Bunuel wrote:
$$(2 + x)(2 + y) – (2 + x) – (2 + y) =$$

(A) 2y
(B) xy
(C) x + y
(D) x – y
(E) x + y + xy

=====

All we need to do is simplify this expression.

Multiply (2 + x)(2 + y) using FOIL. [First Outer Inner Last] and simplify

(2 + x)(2 + y) - (2 + x) - (2 + y)
4 + 2x + 2y + yx - 2 - x - 2 - y
x + y + yx

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Kudos [?]: 54 [0], given: 142

Manager
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Re: (2 + x)(2 + y) – (2 + x) – (2 + y) = [#permalink]

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27 Aug 2017, 03:05
took (2+x) common from the first two elements

so (2+x)(2+y) -(2+x)-(2+y)= (2+x) ((2+y)-1) -(2+y)
=(2+x)(1+y)-(2+y)
=2+2y+x+xy-2-y
=x+y+xy

Kudos [?]: 13 [0], given: 85

Re: (2 + x)(2 + y) – (2 + x) – (2 + y) =   [#permalink] 27 Aug 2017, 03:05
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