Answer
$2y(3x-5y)(9x^2+15xy+25y^2)$
Work Step by Step
Factoring the $GCF=
2y
$, then the given expression, $
54x^3y-250y^4
$ is equivalent to
\begin{array}{l}
2y(27x^3-125y^3)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of $2$ cubes, then the factored form of the expression, $
2y(27x^3-125y^3)
$ is
\begin{array}{l}
2y(3x-5y)[(3x)^2-(3x)(-5y)+(-5y)^2]
\\\\=
2y(3x-5y)(9x^2+15xy+25y^2)
.\end{array}
