Answer
$9m^2-12m+4+6mp-4p+p^2$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
[(3m-2)+p]^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3m-2)^2+2(3m-2)(p)+(p)^2
\\\\=
(3m-2)^2+2p(3m-2)+p^2
\\\\=
(3m-2)^2+6mp-4p+p^2
\\\\=
[(3m)^2+2(3m)(-2)+(-2)^2]+6mp-4p+p^2
\\\\=
9m^2-12m+4+6mp-4p+p^2
.\end{array}
