yea, I originally had the problem like this..
\(\displaystyle (1 + x + x^{2} +...+x^{9})(1+x^{5}+x^{10}+x^{15}+...+x^{100})(1+x^{10}+x^{20}+x^{30}+...+x^{100})\)
I then reduced the first expression to :
\(\displaystyle (1-x^{10}/1-x)\) left the second expression untouched, and reduced the third to, \(\displaystyle (1/1-x^{10})\) .
I actually have the problem worked out, but the last line where the professor got the answer left me blank, because I cant see how he got 21 so easily.