Number of Distinct Terms in an Expansion

Question

1) Determine the coefficient of $v^3w^2x^3z$ in the expansion of $$(v + 2w − 2x + y + z)^9.$$

2) How many distinct terms arise in the expansion?

For #1 I got $-161280$ as the answer. How do I do #2?

Answer 1

Your result for #1 is correct, as regards #2 note that in the expansion of $(v + 2w − 2x + y + z)^9$ we will obtain terms of the form $\text{coeff}\cdot v^aw^bx^cy^dz^e$ where $a,b,c,d,e$ are non negative integers such that $$a+b+c+d+e=9.$$ Now use Stars and bars.