## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x^4(x+2y)(x-y)$
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}