# Binomial theorem - number of terms in expansion

Question: Find the number of terms, after simplifying, in $$(x + y + \frac{1}{x} + \frac{1}{y})^{16}$$

I was unable to find any approach to this question. Fully expanding the expression isn't a viable solution. A hint to start the problem would be appreciated.

$$x+y+\frac1x+\frac1y=\frac{(x+y)(1+xy)}{xy}$$
Now, $(a+b)^n$ has $n+1$ terms for integer $n\ge0$
• @Gummybears. When you see problems like this one, be sure that there is a trick. Consider you are lucky with the power $16$; they could have asked that question with power $12345$ ! – Claude Leibovici Dec 6 '14 at 7:40