Answer
$a(b^2+9a^2)(b+3a)(b-3a)$
Work Step by Step
Factoring the $GCF=
a
$, then the given expression, $
b^4a-81a^5
$ is equivalent to
\begin{array}{l}
a(b^4-81a^4)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the factored form of the given expression, $
a(b^4-81a^4)
$, is
\begin{array}{l}
a(b^2+9a^2)(b^2-9a^2)
\\\\=
a(b^2+9a^2)(b+3a)(b-3a)
.\end{array}
