Answer
$(5a-12)^2$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
25a^2-120a+144
\end{align*} has $ac=
25(144)=3600
$ and $b=
-120
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-60,-60
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
25a^2-60a-60a+144
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(25a^2-60a)-(60a-144)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
5a(5a-12)-12(5a-12)
.\end{align*}
Factoring the $GCF=
(5a-12)
$ of the entire expression above results to
\begin{align*}
&
(5a-12)(5a-12)
\\&=
(5a-12)^2
.\end{align*}
The factored form of the given expression is $
(5a-12)^2
$.
