Answer
$(m+15n)(m-10n)$
Work Step by Step
The given expression is equivalent to
\begin{array}{l}\require{cancel}
5mn+m^2-150n^2
\\\\=
m^2+5mn-150n^2
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the given $\text{
expression
}$
\begin{array}{l}\require{cancel}
m^2+5mn-150n^2
\end{array} has $c=
-150
$ and $b=
5
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
15,-10
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
(m+15n)(m-10n)
.\end{array}
