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Which of the following is equivalent to [m](x + y)(x^2 + y^2)(x^4 + y^
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17 Feb 2021, 05:47
17 Feb 2021, 05:47
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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. \(x^8 - 4x^2y^2 + y^8\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(x - y\)
B. \(x^2 - y^2\)
C. \(x^4 - y^4\)
D. \(x^8 - y^8\)
E. \(x^8 - 4x^2y^2 + y^8\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Which of the following is equivalent to [m](x + y)(x^2 + y^2)(x^4 + y^
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17 Feb 2021, 06:48
17 Feb 2021, 06:48
2
Carcass 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. \(x^8 - 4x^2y^2 + y^8\)
A. \(x - y\)
B. \(x^2 - y^2\)
C. \(x^4 - y^4\)
D. \(x^8 - y^8\)
E. \(x^8 - 4x^2y^2 + y^8\)
APPROACH #1: Recognizing various differences of squares hiding in the expression
Key property: \((a + b)(a - b) = a^2 - b^2\)
Take: \((x + y)(x^2 + y^2)(x^4 + y^4)(x - y)\)
Rearrange: \((x + y)(x - y)(x^2 + y^2)(x^4 + y^4)\)
Multiply the first two sets of brackets: \((x^2 - y^2)(x^2 + y^2)(x^4 + y^4)\)
Multiply: \(x^8 - y^8\)
Answer: D
APPROACH #2: Testing values
Another (slightly 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
Answer: D
General Discussion
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Which of the following is equivalent to [m](x + y)(x^2 + y^2)(x^4 + y^
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17 Feb 2021, 08:16
17 Feb 2021, 08:16
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Carcass 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. \(x^8 - 4x^2y^2 + y^8\)
A. \(x - y\)
B. \(x^2 - y^2\)
C. \(x^4 - y^4\)
D. \(x^8 - y^8\)
E. \(x^8 - 4x^2y^2 + y^8\)
\((x + y)(x - y)(x^2 + y^2)(x^4 + y^4)\)
\((x^2 - y^2)(x^2 + y^2)(x^4 + y^4)\)
\((x^4 - y^4)(x^4 + y^4)\)
\((x^8 - y^8)\)
Hence, option D
