Answer
$3(2-q)(2-3p)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor the $GCF$ of the terms. Then, group the terms of the given expression, $
12-6q-18p+9pq
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Using the $GCF=
3
,$, the expression above is equivalent to
\begin{array}{l}\require{cancel}
3(4-2q-6p+3pq)
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
3[(4-2q)-(6p-3pq)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3[2(2-q)-3p(2-q)]
.\end{array}
Factoring the $GCF=
(2-q)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
3[(2-q)(2-3p)]
\\\\=
3(2-q)(2-3p)
.\end{array}