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12 Aug 2016, 08:59
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
84% (01:12) correct
16%
(01:32)
wrong
based on 254
sessions
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Which of the following is equivalent to \((x + y)(x^2 + y^2)(x^4 + y^4)(x - y)\)?
A. x - y
B. x^2 - y^2
C. x^4 - y^4
D. x^8 - y^8
E. x^8 - 4x^2y^2 + y^8
A. x - y
B. x^2 - y^2
C. x^4 - y^4
D. x^8 - y^8
E. x^8 - 4x^2y^2 + y^8
Updated on: 08 Feb 2021, 14:41
Originally posted by BrentGMATPrepNow on 12 Aug 2016, 12:05.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 14:41, edited 1 time in total.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 14:41, edited 1 time in total.
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Bunuel
The approach that Senthil1981 used is perfect. It recognizes the various DIFFERENCES OF SQUARES hiding in the big expression.
HOWEVER, if you didn't see that approach, another (little longer) approach is the PLUG IN VALUES for x and y and then test the answer choices.
Here's what I mean:
Let's plug x = 2 and y = 1 into the given expression.
We get: (2 + 1)(2² + 1²)(2⁴ + 1⁴)(2 - 1) = (3)(4 + 1)(16 + 1) = (3)(5)(17) = 255
So, when x = 2 and y = 1, (x + y)(x² + y²)(x⁴ + y⁴)(x - y) is equal to 255
So, if an algebraic expression is EQUIVALENT to the given expression, it should evaluate to 255, when we plug in x = 2 and y = 1
Check the answer choices:
A. 2 - 1 = 1 NO GOOD
B. 2² - 1² = 3 NO GOOD
C. 2⁴ - 1⁴ = 15 NO GOOD
D. 2⁸ - 1⁸ = 255 PERFECT!!
E. 2⁸ - 4(2²)(1²) + 1⁸ = 241 NO GOOD
General Discussion
Senthil1981
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 225
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
12 Aug 2016, 09:34
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Given \((x+y)(x^2+y^2)(x^4+y^4)(x−y)\)
Re- arranging the terms \((x+y) ( x- y) (x^2+y^2)(x^4+y^4)\)
= \((x^2-y^2) (x^2+y^2)(x^4+y^4)\)
= \((x^4 - y^4)(x^4+y^4)\)
= \((x^8-y^8)\)
Answer is D
Re- arranging the terms \((x+y) ( x- y) (x^2+y^2)(x^4+y^4)\)
= \((x^2-y^2) (x^2+y^2)(x^4+y^4)\)
= \((x^4 - y^4)(x^4+y^4)\)
= \((x^8-y^8)\)
Answer is D
