Answer
$9x^2+24xy+16y^2$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $
(3x+4y)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3x)^2+2(3x)(4y)+(4y)^2
\\\\=
9x^2+24xy+16y^2
.\end{array}