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51 algebra solving

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Master | Next Rank: 500 Posts
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by ern5231 » Sat Oct 03, 2009 7:46 pm
Solve : Root x^4-2*x^2*y^2+y^4 /(x-y)

I am getting the answer as x+y but the answer given is （x+y)(x+y）^2
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by cbenk121 » Sat Oct 03, 2009 8:45 pm
Hm, well I got (x-y)(x+y)^2; could you double check that (x+y)(x+y)^2 is correct answer? I find it strange, because it could just be written (x+y)^3, and books usually put answer in simplest terms.

Anyway, onto how I got to that answer...

x^4 - 2*x^2*y^2 + y^4

Recognize that? It's in the format a^2 - 2ab + b^2 = (a^2 - b^2)(a^2 - b^2).

So you can factor into...

(x^2-y^2)(x^2-y^2)

Recognize that? Each one of those terms is in the format a^2 - b^2 = (a + b)(a - b).

So you can factor into...

(x+y)(x-y)(x+y)(x-y)

That's all over (x-y), so one of the (x-y) terms on the top cancels out.

You are left with (x-y)(x+y)^2.
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