Answer
$10(c+1)^2$
Work Step by Step
Factoring the negative $GCF=
10
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
10c^2+20c+10
\\\\=
10(c^2+2c+1)
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
10(c^2+2c+1)
\end{array} has $c=
1
$ and $b=
2
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
1,1
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
10(c+1)(c+1)
\\\\=
10(c+1)^2
.\end{array}
