Answer
$8mn(m-3n)(m-1)$
Work Step by Step
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}