#### Answer

$(10x^2+9 )(10x^2-9 )$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
100x^4-81
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
100x^4
$ and $
81
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
100x^4-81
,$ 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}
(10x^2)^2-(9 )^2
\\\\=
(10x^2+9 )(10x^2-9 )
.\end{array}