Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 66

$(mn-8)(mn+4)$

The two numbers whose product is $ac= 1(-32)=-32 $ and whose sum is $b= -4 $ are $\{ -8,4 \}$. Using these two numbers to decompose the middle term of the expression, $ m^2n^2-4mn-32 ,$ then the factored form is \begin{array}{l} m^2n^2-8mn+4mn-32 \\\\= (m^2n^2-8mn)+(4mn-32) \\\\= mn(mn-8)+4(mn-8) \\\\= (mn-8)(mn+4) .\end{array}