#### Answer

$9m^2-30mn+25n^2-p^2$

#### Work Step by Step

Use special products to multiply the given expression, $
[(3m-5n)+p][(3m-5n)-p]
.$
Using $(x+y)(x-y)=x^2-y^2$ or the product of the sum and difference of like terms, the expression above simplifies to
\begin{array}{l}\require{cancel}
(3m-5n)^2-(p)^2
\\\\=
(3m-5n)^2-p^2
.\end{array}
Using $(x+y)^2=x^2+2xy+y^2$ or the square of a binomial, the expression above simplifies to
\begin{array}{l}\require{cancel}
(3m)^2+2(3m)(-5n)+(-5n)^2-p^2
\\\\=
9m^2-30mn+25n^2-p^2
.\end{array}