Answer
$(5x-3)^2$
Work Step by Step
The two numbers whose product is $ac=
25(9)=225
$ and whose sum is $b=
-30
$ are $\{
-15,-15
\}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $
25x^2-30x+9
$,is
\begin{array}{l}\require{cancel}
25x^2-15x-15x+9
\\\\=
(25x^2-15x)-(15x-9)
\\\\=
5x(5x-3)-3(5x-3)
\\\\=
(5x-3)(5x-3)
\\\\=
(5x-3)^2
.\end{array}
