Let \(n\) be a positive integer. The coefficient of \(x^3y^5\) in the expansion of
\[(1+xy+y^2)^n\]
equals
\[(a) \quad n,\quad(b) \quad 2^n,\quad(c) \quad \begin{pmatrix}n\\3\end{pmatrix} \begin{pmatrix}n\\5\end{pmatrix},\quad(d) \quad 4\begin{pmatrix}n\\4\end{pmatrix},\quad(e) \quad\begin{pmatrix}n\\8\end{pmatrix}.\]
Could we write \((1+xy+y^2)^n\) as \((1+y(x+y))^n\)? What happens if we expand this with the binomial theorem now?
