Answer
$\dfrac{4}{9}t^2+12t+81$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the special product on squaring binomials, the given expression, $
\left(\dfrac{2}{3}t+9\right)^2
$, is equivalent to
\begin{align*}\require{cancel}
&
\left(\dfrac{2}{3}t\right)^2+2\left(\dfrac{2}{3}t\right)(9)+9^2
\\\\&=
\dfrac{4}{9}t^2+2\left(\dfrac{2}{\cancelto13}t\right)(\cancelto39)+81
\\\\&=
\dfrac{4}{9}t^2+12t+81
.\end{align*}
Hence, the expression $
\left(\dfrac{2}{3}t+9\right)^2
$ simplifies to $
\dfrac{4}{9}t^2+12t+81
$.
