Answer
$81 m^4 + 108 m^3 n + 54 m^2 n^2 + 12 m n^3 + n^4$
Work Step by Step
Using the Binomial Formula, the expression $
(3m+n)^4
$ expands to
\begin{array}{l}
(3m)^4n^0+
\dfrac{4}{1!}(3m)^3n^1+
\dfrac{4\cdot3}{2!}(3m)^2n^2+
\dfrac{4\cdot3\cdot2}{3!}(3m)^1n^3+\\
\dfrac{4\cdot3\cdot2\cdot1}{4!}(3m)^0n^4
\\\\=
81 m^4 + 108 m^3 n + 54 m^2 n^2 + 12 m n^3 + n^4
\end{array}
