Answer
$x^4(x+2y)(x-y)$
Work Step by Step
Factoring the $GCF=
x^4
$, then the given expression, $
x^6+x^5y-2x^4y^2
$ is equivalent to
\begin{array}{l}
x^4(x^2+xy-2y^2)
.\end{array}
The two numbers whose product is $ac=
1(-2)=-2
$ and whose sum is $b=
1
$ are $\{
2,-1
\}$. Using these two numbers to decompose the middle term of the expression, $
x^4(x^2+xy-2y^2)
,$ then the factored form is
\begin{array}{l}
x^4(x^2+2xy-1xy-2y^2)
\\\\=
x^4[(x^2+2xy)-(1xy+2y^2)]
\\\\=
x^4[x(x+2y)-y(x+2y)]
\\\\=
x^4[(x+2y)(x-y)]
\\\\=
x^4(x+2y)(x-y)
.\end{array}