Answer
$(3a-4)^2$
Work Step by Step
Let $z=(3a+5).$ Then the given expression, $
(3a+5)^2-18(3a+5)+81
,$ is equivalent to
\begin{array}{l}\require{cancel}
z^2-18z+81
.\end{array}
The two numbers whose product is $ac=
1(81)=81
$ and whose sum is $b=
-18
$ are $\{
-9,-9
\}$. Using these two numbers to decompose the middle term of the expression, $
z^2-18z+81
,$ then
\begin{array}{l}\require{cancel}
z^2-9z-9z+81
\\\\=
(z^2-9z)-(9z-81)
\\\\=
z(z-9)-9(z-9)
\\\\=
(z-9)(z-9)
\\\\=
(z-9)^2
.\end{array}
Since $z=(3a+5)$, then the expression $
(z-9)^2
$ is equivalent to
\begin{array}{l}\require{cancel}
(3a+5-9)^2
\\\\=
(3a-4)^2
.\end{array}
