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by vinay1983 » Thu Sep 12, 2013 4:45 pm
What is the value of x^8 + y^8. I recollect seeing similar question in MGMAT tests. Can somebody help me how to approach such problems? As is it there are so many ways to provide the answer, and all can be correct. So how can we know, which is the correct answer!
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by ganeshrkamath » Thu Sep 12, 2013 6:51 pm
vinay1983 wrote:What is the value of x^8 + y^8. I recollect seeing similar question in MGMAT tests. Can somebody help me how to approach such problems? As is it there are so many ways to provide the answer, and all can be correct. So how can we know, which is the correct answer!
Could you please post an example?

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by [email protected] » Thu Sep 12, 2013 9:50 pm
Hi vinay1983,

If you're talking about "simplifying" or "rewriting" x^8 + y^8, then there isn't an option that the GMAT would expect you to know.

However, you CAN rewrite x^8 - y^8 since this is an complex example of a Classic Quadratic: The difference of squares.

x^8 - y^8 = (x^4 + y^4)(x^4 - y^4)

Then x^4 - y^4 can be rewritten as (x^2 + y^2)(x^2 - y^2)

THEN x^2 - y^2 can be rewritten as (x + y)(x - y)

So x^8 - y^8 = (x^4 + y^4)(x^2 + y^2)(x + y)(x - y)

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