Binomial theorem - number of terms in expansion

Question

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.

Answer 1

HINT:

$$x+y+\frac1x+\frac1y=\frac{(x+y)(1+xy)}{xy}$$

Now, $(a+b)^n$ has $n+1$ terms for integer $n\ge0$