Answer
$c^2+10 c+25=(c+5)^2$
Work Step by Step
Given\begin{equation}
c^2+10 c+25.
\end{equation} Factor the quadratic as shown below. $ 25$ is a perfect square and can be factored as $5\times 5= 25$. We see that $5+5= 10$ which is what we want to get the middle term. Hence:
\begin{equation}
\begin{aligned}
c^2+10 c+25&= c^2+5 c+5c+25\\
& =2\left[c (c+5)+5(c+5)\right]\\
& = (c+5)(c+5)\\
&= (c+5)^2.
\end{aligned}
\end{equation} The factored form of the quadratic is:
\begin{equation}c^2+10 c+25=(c+5)^2.
\end{equation}
