Question

What is the complete factorization of p(x)=32x5y−2xy5 over the integers?

Answer 1

`p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)`

Explanation:

`p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}`

__

The factoring of the difference of squares is applicable:

a^2 -b^2 = (a -b)(a +b)