Answer
$(4+9k)(4-9k)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
16-81k^2
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
16
$ and $
81k^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
16-81k^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}
(4)^2-(9k)^2
\\\\=
(4+9k)(4-9k)
.\end{array}
