Answer
$7(p^2+q^2)(p+q)(p-q)$
Work Step by Step
Factoring the $GCF=
7
$, then the given expression, $
7p^4-7q^4
$ is equivalent to
\begin{array}{l}
7(p^4-q^4)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the complete factored form of the expression above is
\begin{array}{l}
7(p^2+q^2)(p^2-q^2)
\\\\=
7(p^2+q^2)(p+q)(p-q)
.\end{array}
