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X^8 - Y^8 =
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13 Jul 2010, 18:42
13 Jul 2010, 18:42
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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. \((X^2 - Y^2)^4\)
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. \((X^2 - Y^2)^4\)
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Joined: 09 Jun 2010
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Posts: 1763
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Concentration: General Management, Nonprofit
Schools: HBS '17 (M) Stanford '17 (A)
Re: MGMAT Challenge Problem
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14 Jul 2010, 06:13
14 Jul 2010, 06:13
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The solution is just a basic application of the principle that \(x^2 - y^2 = (x+y)(x-y)\)
So, when we simplify, we treat \(x^8 = (x^4)^2 = ((x^2)^2)^2\)
So we get the following:
\(x^8 - y^8 = (x^4+y^4)(x^4-y^4) = (x^4+y^4)(x^2+y^2)(x^2 - y^2) =(x^4+y^4)(x^2+y^2)(x+y)(x-y)\)
So, the answer is B.
So, when we simplify, we treat \(x^8 = (x^4)^2 = ((x^2)^2)^2\)
So we get the following:
\(x^8 - y^8 = (x^4+y^4)(x^4-y^4) = (x^4+y^4)(x^2+y^2)(x^2 - y^2) =(x^4+y^4)(x^2+y^2)(x+y)(x-y)\)
So, the answer is B.
Re: MGMAT Challenge Problem
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13 Jul 2010, 19:39
13 Jul 2010, 19:39
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Apply a^2 - b^2 = (a-b)(a+b)
(x^4)^2 - (y^4)^2
( x^4 + y^4) ( x^4 - y^4)
( x^4 + y^4) (x^2+y^2)(x^2-y^2)
( x^4 + y^4) (x^2+y^2)(x+y)(x-y)
So B
(x^4)^2 - (y^4)^2
( x^4 + y^4) ( x^4 - y^4)
( x^4 + y^4) (x^2+y^2)(x^2-y^2)
( x^4 + y^4) (x^2+y^2)(x+y)(x-y)
So B
