Answer
$27-36i$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression $
9(2-i)^2
$ simplifies to
\begin{array}{l}
9[(2)^2+2(2)(-i)+(-i)^2]
\\=
9[4-4i+i^2]
\\=
9[4-4i+(-1)]
\\=
9[3-4i]
\\=
27-36i
.\end{array}