Answer
$x^2+16xy+64y^2$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $
(x+8y)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x)^2+2(x)(8y)+(8y)^2
\\\\=
x^2+16xy+64y^2
.\end{array}