Answer
$m^2+2mp+p^2-25$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $
[(m+p)-5][(m+p)+5]
,$ is equivalent to
\begin{array}{l}\require{cancel}
(m+p)^2-(5)^2
\\\\=
(m+p)^2-25
.\end{array}
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above is equivalent to
\begin{array}{l}\require{cancel}
[(m)^2+2(m)(p)+(p)^2]-25
\\\\=
m^2+2mp+p^2-25
.\end{array}
