#### Answer

$2(5p+9)(5p-9)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
50p^2-162
,$ 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 $
2
,$ 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}
2(25p^2-81)
.\end{array}
The expressions $
25p^2
$ and $
81
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
25p^2-81
,$ 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}
2[(5p)^2-(9)^2]
\\\\=
2[(5p+9)(5p-9)]
\\\\=
2(5p+9)(5p-9)
.\end{array}