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