Answer
$16x^4+32x^3y+24x^2y^2+8xy^3+y^4$
Work Step by Step
Using the coefficients in the $r=5$ row of the Pascal's triangle, $\left\{
1,4,6,4,1
\right\}$, and the pattern in expanding binomials, then $
(2x+y)^4
$ expands to
\begin{array}{l}
(2x)^4y^0+4(2x)^3y^1+6(2x)^2y^2+4(2x)^1y^3+(2x)^0y^4
\\\\=
16x^4+32x^3y+24x^2y^2+8xy^3+y^4
.\end{array}
