Question

Factorize `x^4 + 2x^3y - 2xy^3 – y^4 =` ?

Answer 1

See below.

Explanation:

Making `y = lambda x` and substituting

`x^4+2x^4 lambda-2x^4lambda^3-x^4lambda^4=x^4(1+2lambda-2lambda^3-lambda^4)=-x^4(1 + lambda^2) ( lambda^2- 2 lambda-1)=-x^4(1+lambda^2)(lambda-1-sqrt2)(lambda-1+sqrt2)` so

replacing again `lambda=y/x` we get

`x^4 + 2x^3y - 2xy^3 – y^4 =-(x^2+y^2)(y-(1+sqrt2)x)(y-(1-sqrt2)x)`