Answer
$(9m^2+4p^2)(3m+2p)(3m-2p)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
81m^4-16p^4
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
81m^4
$ and $
16p^4
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
81m^4-16p^4
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares, which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(9m^2)^2-(4p^2)^2
\\\\=
(9m^2+4p^2)(9m^2-4p^2)
.\end{array}
The expressions $
9m^2
$ and $
4p^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
9m^2-4p^2
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares, which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(9m^2+4p^2)[(3m)^2-(2p)^2]
\\\\=
(9m^2+4p^2)(3m+2p)(3m-2p)
.\end{array}
