Answer
$2(5x+2y)(25x^2-10xy+4y^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
250x^3+16y^3
,$ factor first the $GCF$. Then use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=
2
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
2(125x^3+8y^3)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or $a^3-b^3=(a-b)(a^2+ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
2(5x+2y)[(5x)^2-5x(2y)+(2y)^2]
\\\\=
2(5x+2y)(25x^2-10xy+4y^2)
.\end{array}
