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
I am getting the answer as x+y but the answer given is （x+y)(x+y）^2
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.
