Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 248: 40

$2xy(4x+3y)(4x-3y)$

Factoring out the greatest common factor of 2xy, the given expression, $ 32x^3y-18xy^3 ,$ is equivalent to \begin{array}{l}\require{cancel} 2xy(16x^2-9y^2) .\end{array} Using $a^2-b^2=(a+b)(a-b)$, the completely factored form of the expression above is \begin{array}{l}\require{cancel} 2xy(4x+3y)(4x-3y) .\end{array}