Answer
$4qb \left( 3q+2b-5q^2b \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
12q^2b+8qb^2-20q^3b^2
,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
12,8,-20
\}$ is $
4
$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
q^2b, qb^2,q^3b^2
\}$ is $
qb
.$ Hence, the entire expression has $GCF=
4qb
.$
Factoring the $GCF=
4qb
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
4qb \left( \dfrac{12q^2b}{4qb}+\dfrac{8qb^2}{4qb}-\dfrac{20q^3b^2}{4qb} \right)
\\\\=
4qb \left( 3q+2b-5q^2b \right)
.\end{array}
