I'm a little on how the binomial theorem works. I have a problem where

Given that $\displaystyle (1+x^2)+(1+x^2)^2+...+(1+x^2)^{20}$,compute the coefficient of $\displaystyle x^2$.

I know in the binomial theorem I can set x to 1 and y to x to have

$\displaystyle (1+x)^n$ but do I have to do this 20 times to find when n=1,2,3 etc?