Answer
$16x^4+32x^3y+24x^2y^2+8xy^3+y^4$
Work Step by Step
We are given the expression $(2x+y)^4$.
For expanding it we will use the $\textit{Binomial Theorem}$:
$$\begin{align}(a+b)^n=\binom{n}{0}a^n+\binom{n}{1}a^{n-1}b+\binom{n}{2}a^{n-2}b^2+\cdots+\binom{n}{n}b^n.\end{align}\tag1$$
Substitute $a=1$, $b=-x^2$, $n=6$ in Eq. $(1)$:
$$\begin{align*}
(2x+y)^4&=\binom{4}{0}(2x)^4+\binom{4}{1}(2x)^3y+\binom{4}{2}(2x)^2y^2\\
&\phantom{=}+\binom{4}{1}(2x)y^3+\binom{4}{4}y^4\\
&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4.
\end{align*}$$
The expansion is:
$$(2x+y)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4.$$
