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

$4c(5d-c)(4d-c)$
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}