Answer
$(5a-6)^2$
Work Step by Step
Let $z=(5a-3)$. Then the given expression, $
(5a-3)^2-6(5a-3)+9
$, is equivalent to
\begin{array}{l}
z^2-6z+9
.\end{array}
The two numbers whose product is $ac=
1(9)=9
$ and whose sum is $b=
-6
$ are $\{
-3,-3
\}$. Using these two numbers to decompose the middle term of the expression, $
z^2-6z+9
$, results to
\begin{array}{l}
z^2-3z-3z+9
\\\\=
(z^2-3z)-(3z-9)
\\\\=
z(z-3)-3(z-3)
\\\\=
(z-3)(z-3)
\\\\=
(z-3)^2
.\end{array}
Since $z=(5a-3)$, then,
\begin{array}{l}
(z-3)^2
\\\\=
(5a-3-3)^2
\\\\=
(5a-6)^2
.\end{array}
