Answer
$2(4t^2+9y^2)(2t+3y)(2t-3y)$
Work Step by Step
Factoring the $GCF=
2
$, then the given expression, $
32t^4-162y^4
$ is equivalent to
\begin{array}{l}
2(16t^4-81y^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}
2(4t^2+9y^2)(4t^2-9y^2)
\\\\=
2(4t^2+9y^2)(2t+3y)(2t-3y)
.\end{array}
