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Which of the following equals x + xy + (x + xy)y?
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21 Nov 2019, 00:47
21 Nov 2019, 00:47
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Which of the following equals \(x + xy + (x + xy)y\)?
(A) \(x(1 + y)^2\)
(B) \(x(2 + y + y^2)\)
(C) \(2x(1 + y) + y\)
(D) \(2xy(1 + y)\)
(E) \(x^2(1 + y^2)y\)
(A) \(x(1 + y)^2\)
(B) \(x(2 + y + y^2)\)
(C) \(2x(1 + y) + y\)
(D) \(2xy(1 + y)\)
(E) \(x^2(1 + y^2)y\)
Senior Manager
Joined: 13 Feb 2018
Posts: 385
Given Kudos: 50
GMAT 1: 640 Q48 V28
Which of the following equals x + xy + (x + xy)y?
[#permalink]
21 Nov 2019, 01:04
21 Nov 2019, 01:04
1
Kudos
2 ways to solve. First pure algebra (my least beloved thing and most needed on Gmat 
) and second brute force (I like to waste up to 5 minutes brute-forcing everything )
1) Algebra
x+xy+(x+xy)y
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
factor out common variable: \(x(1+2y+y^2)\)
Observe that \(1+2y+y^2=(1+y)^2\)
So we have \(x(1+y)^2\)
Look for such option
2) Brute force
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
Open the brackets for every answer choice to see the match
Hope you will choose the first option and score 700+ on actual test
Have a nice day
L
) and second brute force (I like to waste up to 5 minutes brute-forcing everything )1) Algebra
x+xy+(x+xy)y
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
factor out common variable: \(x(1+2y+y^2)\)
Observe that \(1+2y+y^2=(1+y)^2\)
So we have \(x(1+y)^2\)
Look for such option
2) Brute force
Open the brackets: \(x+xy+xy+xy^2\)=\(x+2xy+xy^2\)
Open the brackets for every answer choice to see the match
Hope you will choose the first option and score 700+ on actual test
Have a nice day
L
VP
Joined: 16 Feb 2015
Posts: 1079
Given Kudos: 30
Location: United States
Re: Which of the following equals x + xy + (x + xy)y?
[#permalink]
21 Nov 2019, 21:06
21 Nov 2019, 21:06
Bunuel wrote:
Which of the following equals \(x + xy + (x + xy)y\)?
(A) \(x(1 + y)^2\)
(B) \(x(2 + y + y^2)\)
(C) \(2x(1 + y) + y\)
(D) \(2xy(1 + y)\)
(E) \(x^2(1 + y^2)y\)
(A) \(x(1 + y)^2\)
(B) \(x(2 + y + y^2)\)
(C) \(2x(1 + y) + y\)
(D) \(2xy(1 + y)\)
(E) \(x^2(1 + y^2)y\)
Explanation:
Approach, opening the brackets, taking common out as in option, common is out
= x + xy + (x+xy).y
= x + xy + xy + xy^2
Taking x (common out)
= x (1+ 2y + y^2)
= x ( 1 + y)^2--- Option A
Please give kudos, if you find my explanation good enough 
