Answer
$4c(5d-c)(4d-c)$
Work Step by Step
Factoring the $GCF=
4c
$, then the given expression, $
80cd^2-36c^2d+4c^3
$ is equivalent to
\begin{array}{l}
4c(20d^2-9cd+c^2)
.\end{array}
The two numbers whose product is $ac=
20(1)=20
$ and whose sum is $b=
-9
$ are $\{
-4,-5
\}$. Using these two numbers to decompose the middle term of the expression, $
4c(20d^2-4cd-5cd+c^2)
,$ then the factored form is
\begin{array}{l}
4c[(20d^2-4cd)-(5cd-c^2)]
\\\\=
4c[4d(5d-c)-c(5d-c)]
\\\\=
4c[(5d-c)(4d-c)]
\\\\=
4c(5d-c)(4d-c)
.\end{array}
