Answer
$x^6 + 18 x^5 y + 135 x^4 y^2 + 540 x^3 y^3 + 1215 x^2 y^4 + 1458 x y^5 + 729 y^6
$
Work Step by Step
Using the Binomial Formula, the expression $
(x+3y)^6
$ expands to
\begin{array}{l}
x^6(3y)^0+
\dfrac{6}{1!}x^5(3y)^1+
\dfrac{6\cdot5}{2!}x^4(3y)^2+
\dfrac{6\cdot5\cdot4}{3!}x^3(3y)^3+
\dfrac{6\cdot5\cdot4\cdot3}{4!}x^2(3y)^4+
\dfrac{6\cdot5\cdot4\cdot3\cdot2}{5!}x^1(3y)^5+
\dfrac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{6!}x^0(3y)^6+
\\\\\\=
x^6 + 18 x^5 y + 135 x^4 y^2 + 540 x^3 y^3 + 1215 x^2 y^4 + 1458 x y^5 + 729 y^6
\end{array}