Answer
$4(y+1)(y-2)$
Work Step by Step
Factoring the $GCF=
4
,$ the given expression, $
4y^2-4y-8
,$ is equivalent to
\begin{array}{l}\require{cancel}
4(y^2-y-2)
.\end{array}
The trinomial expression above has $c=
-2
$ and $b=
-1
.$
The possible factors of $c$ are $
\{ 1,-2 \}
,\{ -1,2 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
1,-2
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
4(y+1)(y-2)
.\end{array}