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If xy 0 and x -y, =

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sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4804

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

If xy 0 and x -y, = [#permalink]

19 May 2018, 15:13

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Question Stats:

95% (00:58) correct

4% (01:03) wrong

based on 21 sessions

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If $xy \neq 0$ and $x \neq -y$,$\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}$ =

(A) $1$
(B) $x^2 - y^2$
(C) $x^9 - y^9$
(D) $x^{18} - y^{18}$
(E) $\frac{1}{x^9 - y^9}$

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mohan514

Manager

Joined: 26 Jan 2018

Posts: 189

GRE 1: Q165 V156

Re: If xy 0 and x -y, = [#permalink]

21 May 2018, 21:24

(a+b)*(a-b)= a^2-b^2.
Using this formula to further solve the above equation leaves us with option C

cristianrosales

Intern

Joined: 25 Aug 2020

Posts: 17

Re: If xy 0 and x -y, = [#permalink]

27 Sep 2020, 11:33

Can someone explain this in more detail? I'm not sure what to do on this one

GreenlightTestPrep

GRE Instructor

Joined: 10 Apr 2015

Posts: 4395

Re: If xy 0 and x -y, = [#permalink]

03 Oct 2020, 10:23

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sandy wrote:

If $xy \neq 0$ and $x \neq -y$,$\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}$ =

(A) $1$
(B) $x^2 - y^2$
(C) $x^9 - y^9$
(D) $x^{18} - y^{18}$
(E) $\frac{1}{x^9 - y^9}$

$\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}=\frac{(x^{18}+y^{18})(x^{18}-y^{18})}{(x^{18}+y^{18})(x^{9}+y^{9})}$

$=\frac{(x^{18}-y^{18})}{(x^{9}+y^{9})}$

$=\frac{(x^{9}+y^{9})(x^{9}-y^{9})}{(x^{9}+y^{9})}$

$=x^{9}-y^{9}$

Answer: C
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