Answer
$rs(s+4)(s^2-4s+16)$
Work Step by Step
Factoring the $GCF=
rs
,$ the given expression, $
rs^4+64rs
,$ is equivalent to
\begin{array}{l}
rs(s^3+64)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $
rs(s^3+64)
,$ is
\begin{array}{l}
rs(s+4)[ (s)^2-(s)(4)+(4)^2]
\\\\=
rs(s+4)(s^2-4s+16)
.\end{array}