Answer
$(3x-5y)^2$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
9x^2-30xy+25y^2
\end{align*} has $ac=
9(25)=225
$ and $b=
-30
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-15,-15
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
9x^2-15xy-15xy+25y^2
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(9x^2-15xy)-(15xy-25y^2)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
3x(3x-5y)-5y(3x-5y)
.\end{align*}
Factoring the $GCF=
(3x-5y)
$ of the entire expression above results to
\begin{align*}
&
(3x-5y)(3x-5y)
\\&=
(3x-5y)^2
.\end{align*}
Hence, the factored form of $
9x^2-30xy+25y^2
$ is $
(3x-5y)^2
$.
