#### Answer

$(p+q)(p-4z)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
p^2-4zq+pq-4pz
,$ 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.
$\bf{\text{Solution Details:}}$
Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(p^2+pq)-(4zq+4pz)
.\end{array}
Factoring the $GCF$ in each group, results to
\begin{array}{l}\require{cancel}
p(p+q)-4z(q+p)
\\\\=
p(p+q)-4z(p+q)
.\end{array}
Factoring the $GCF=
(p+q)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(p+q)(p-4z)
.\end{array}