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(x^6 * y^6 - x^6 * y^2) / (x^2 + y^2) = ?

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by chetan.sharma » Thu Jan 14, 2016 8:10 am
lee3381 wrote:(x^6 * y^6 - x^6 * y^2) / (x^2 + y^2) = ?

The answer is (xy)^2 * (y^2 - x^2).

but I am just not sure how to get this answer.
anyone can explain this answer?
Hi,
firstly I'll have to change the equation that you have written, because the answer cannot be what you are saying..

(x^6 * y^6 - x^6 * y^2) / (x^2 + y^2) ... should be
(x^2 * y^6 - x^6 * y^2) / (x^2 + y^2) ..

now lets work on it..
(x^2 * y^6 - x^6 * y^2) / (x^2 + y^2) ..
x^2*y^2*(y^4-x^4)/(x^2 + y^2)...
now y^4-x^4 can be written as (x^2 + y^2)(y^2-x^2)...
x^2*y^2*(x^2 + y^2)(y^2-x^2)/(x^2 + y^2)= (xy)^2 * (y^2 - x^2)..

hope it helps
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by Matt@VeritasPrep » Fri Jan 22, 2016 4:58 pm
I think Chetan is right. We should have:

(x²y� - x�y²) / (x² + y²), or

(xy)²(y� - x�) / (x² + y²), or

using the difference of squares

(xy)² * (y² + x²) * (y² - x²) / (x² + y²), or

(xy)² * (y² - x²)
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by [email protected] » Fri Jan 22, 2016 7:25 pm
Hi lee3381,

What is the source of this question? Is it a GMAT source or a general 'math' source? I ask because while the basic math concepts (exponents, factoring, Classic Quadratics) will appear on Test Day, the 'design' of this question is not one that you'll likely see.

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