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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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12 Aug 2016, 11:05

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

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