Answer
$4(3b+2)(3b-2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
36b^2-16
,$ factor first the $GCF.$ Then use the factoring of the sum or difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The $GCF$ of the terms is $GCF=
4
$ since it is the highest expression that can evenly divide (no remainder) all the given terms. Factoring the $GCF,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
4(9b^2-4)
.\end{array}
The expressions $
9b^2
$ and $
4
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
9b^2-4
,$ 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[(3b)^2-(2)^2]
\\\\=
4[(3b+2)(3b-2)]
\\\\=
4(3b+2)(3b-2)
.\end{array}
