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# Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)

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Joined: 02 Sep 2009
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Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)  [#permalink]

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12 Aug 2016, 08:59
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15% (low)

Question Stats:

84% (01:32) correct 16% (01:08) wrong based on 139 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

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Re: Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)  [#permalink]

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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 $$(x+y) ( x- y) (x^2+y^2)(x^4+y^4)$$
= $$(x^2-y^2) (x^2+y^2)(x^4+y^4)$$
= $$(x^4 - y^4)(x^4+y^4)$$
= $$(x^8-y^8)$$
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Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)  [#permalink]

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12 Aug 2016, 12:05
Top Contributor
Bunuel wrote:
Which of the following is equivalent to (x + y)(x² + y²)(x⁴ + y⁴)(x - y)?

A. x - y
B. x² - y²
C. x⁴ - y⁴
D. x⁸ - y⁸
E. x⁸ - 4x²y² + y⁸

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

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

RELATED (TRICKY) PRACTICE QUESTION:

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Re: Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)  [#permalink]

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21 Aug 2018, 00:36
Bunuel wrote:
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

Dear Moderator,
While going through the DS section of Algebra, found this PS question. Hope you will do the needful. Thank you.
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GMAT 1: 620 Q50 V24
GMAT 2: 650 Q49 V29
GMAT 3: 650 Q49 V31
GMAT 4: 680 Q48 V35
Re: Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4)  [#permalink]

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21 Aug 2018, 00:45
(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)
Re: Which of the following is equivalent to (x + y)(x^2 + y^2)(x^4 + y^4) &nbs [#permalink] 21 Aug 2018, 00:45
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