Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 248: 39

$3xy(5x+2y)(5x-2y)$

Factoring out the greatest common factor of 3xy, the given expression, $ 75x^3y-12xy^3 ,$ is equivalent to \begin{array}{l}\require{cancel} 3xy(25x^2-4y^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} 3xy(5x+2y)(5x-2y) .\end{array}