Answer
$y^2(y+8)(y-10)$
Work Step by Step
Factoring the $GCF=
y^2
,$ the given expression, $
y^4+2y^3-80y^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
y^2(y^2-2y-80)
.\end{array}
The trinomial expression above has $c=
-80
$ and $b=
-2
.$
The possible factors of $c$ are $
\{ 1,-80 \}
,\{ 2,-40 \}
,\{ 4,-20 \}
,\{ 5,-16 \}
,\{ 8,-10 \}
,\{ -1,80 \}
,\{ -2,40 \}
,\{ -4,20 \}
,\{ -5,16 \}
,\{ -8,10 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
8,-10
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
y^2(y+8)(y-10)
.\end{array}
