Answer
The solution below shows that $(x+y)^4$ is not equal to $x^4+y^4.$
Work Step by Step
Substituting $x=3$ and $y=4,$ the given expression, $
(x+y)^4
,$ evaluates to
\begin{array}{l}\require{cancel}
(3+4)^4
\\\\=
(7)^4
\\\\=
2,401
,\end{array}
while the given expression, $
x^4+y^4
,$ evaluates to
\begin{array}{l}\require{cancel}
3^4+4^4
\\\\=
81+256
\\\\=
337
.\end{array}