SOLUTION: what is x2+2xy-y2 in factored form?

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Question 535675: what is x2+2xy-y2 in factored form?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2xy%2By%5E2=%28x%2By%29%5E2 would be a popular, easier factorization, but

and that looks strange.
It can be calculated as

or as
x%5E2%2B2xy-y%5E2=y%5E2%28%28x%2Fy%29%5E2%2B2%28x%2Fy%29-1%29=y%5E2%28z%5E2%2B2z-1%29 with z=x%2Fy
finding the roots of the polynomial %28z%5E2%2B2z-1%29 with the quadratic formula as

Then
%28z%5E2%2B2z-1%29=%28z%2B1%2Bsqrt%282%29%29%28z%2B1%2Bsqrt%282%29%29 and