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

$8mn(m-3n)(m-1)$
Factoring the $GCF= 8mn$, then the given expression, $8m^3n-32m^2n^2+24mn$ is equivalent to \begin{array}{l} 8mn(m^2-4mn+3) .\end{array} The two numbers whose product is $ac= 1(3)=3$ and whose sum is $b= -4$ are $\{ -3,-1 \}$. Using these two numbers to decompose the middle term of the expression, $8mn(m^2-4mn+3) ,$ then the factored form is \begin{array}{l} 8mn(m^2-3mn-1mn+3) \\\\= 8mn[(m^2-3mn)-(1mn-3)] \\\\= 8mn[m(m-3n)-(mn-3)] \\\\= 8mn[(m-3n)(m-1)] \\\\= 8mn(m-3n)(m-1) .\end{array}