Review question

# What is the coefficient of $x^3y^5$ in the expansion of $(1+xy+y^2)^n$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5965

## Suggestion

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?