## Intermediate Algebra (12th Edition)

$2(5p+9)(5p-9)$
$\bf{\text{Solution Outline:}}$ 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}