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

$2y(3x-5y)(9x^2+15xy+25y^2)$
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}