Answer
$(9x^2+4y^2)(3x+2y)(3x-2y)$
Work Step by Step
Using $a^2-b^2=(a+b)(a-b)$, the factored form of the given expression, $
81x^4-16y^4
,$ is
\begin{array}{l}\require{cancel}
(9x^2+4y^2)(9x^2-4y^2)
.\end{array}
Since the second factor is still a difference of $2$ squares, using the same factoring technique, the completely factored form of the expression above is
\begin{array}{l}\require{cancel}
(9x^2+4y^2)(3x+2y)(3x-2y)
.\end{array}