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X^8 - Y^8 =
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17 Feb 2021, 05:43
17 Feb 2021, 05:43
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79% (00:54) correct
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\(X^8 - Y^8 =\)
A. \((X^4 - Y^4)^2\)
B. \((X^4 + Y^4)(X^2 + Y^2)(X + Y)(X - Y)\)
C. \((X^6 + Y^2)(X^2 - Y^6)\)
D. \((X^4 - Y^4)(X^2 - Y^2)(X - Y)(X + Y)\)
E. \((X^2 - Y^2)^4\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \((X^4 - Y^4)^2\)
B. \((X^4 + Y^4)(X^2 + Y^2)(X + Y)(X - Y)\)
C. \((X^6 + Y^2)(X^2 - Y^6)\)
D. \((X^4 - Y^4)(X^2 - Y^2)(X - Y)(X + Y)\)
E. \((X^2 - Y^2)^4\)
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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Re: X^8 - Y^8 =
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17 Feb 2021, 06:35
17 Feb 2021, 06:35
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Carcass wrote:
\(X^8 - Y^8 =\)
A. \((X^4 - Y^4)^2\)
B. \((X^4 + Y^4)(X^2 + Y^2)(X + Y)(X - Y)\)
C. \((X^6 + Y^2)(X^2 - Y^6)\)
D. \((X^4 - Y^4)(X^2 - Y^2)(X - Y)(X + Y)\)
E. \((X^2 - Y^2)^4\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \((X^4 - Y^4)^2\)
B. \((X^4 + Y^4)(X^2 + Y^2)(X + Y)(X - Y)\)
C. \((X^6 + Y^2)(X^2 - Y^6)\)
D. \((X^4 - Y^4)(X^2 - Y^2)(X - Y)(X + Y)\)
E. \((X^2 - Y^2)^4\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Since \((X^4)^2 = X^8\), and \((Y^4)^2 = Y^8\), we can see that \(X^8 - Y^8\) is a difference of squares
So, \(X^8 - Y^8 =(X^4 + Y^4)(X^4 - Y^4)\)
Scan the answer choices....not there!!
Aha, now we must recognize that \(X^4 - Y^4\) is a difference of squares, which we can factor to get:
\((X^4 + Y^4)(X^4 - Y^4) = (X^4 + Y^4)(X^2 + Y^2)(X^2 - Y^2)\)
Since \(X^2 - Y^2\) is another difference of squares, we can continue factoring to get...
\((X^4 + Y^4)(X^2 + Y^2)(X^2 - Y^2)=(X^4 + Y^4)(X^2 + Y^2)(X+Y)(X-Y)\)
Answer: B
Re: X^8 - Y^8 =
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02 Sep 2024, 10:00
02 Sep 2024, 10:00
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