#### Answer

$9(5k+2r)(5k-2r)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
225k^2-36r^2
,$ factor first the $GCF.$ Then use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The $GCF$ of the terms in the given expression is $
9
,$ since it is the greatest expression that can divide all the terms evenly (no remainder.) Factoring the $GCF$ results to
\begin{array}{l}\require{cancel}
9(25k^2-4r^2)
.\end{array}
The expressions $
25k^2
$ and $
4r^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
25k^2-4r^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}
9[(5k)^2-(2r)^2]
\\\\=
9[(5k+2r)(5k-2r)]
\\\\=
9(5k+2r)(5k-2r)
.\end{array}