Solve for the coefficient of an even generating function Using a generating function, find the number of ways to select 10 candies from a huge pile of red, blue, and green lollipops if the selection has an even number of blue lollipops.
I started, but I don't understand how to continue
$(1 + x + x^2 + x^3 ...)^2 \cdot (1 + x^2 + x^4 + x^6 ...)$
$=(\frac{1}{1-x})^2 \cdot \frac{1}{1-x^2}$
$=\big(1 + \binom{1 + 2 - 1}{1}x + \binom{2 + 2 - 1}{2}x^2 ...\big) \cdot ???$
How do you find coefficient to $x^{10}$? 
Also, our textbook tells us $(1 + x^2 + x^4 + x^6 ...)$ = $\frac{1}{1-x^2}$ how?

Notice that $\left(\frac{1}{1-x}\right)^2=\frac{d}{dx}\left(\frac{1}{1-x}\right)$, and hence $\left(\frac{1}{1-x}\right)^2=1+2x+3x^2+\dots$ You can then find the $x^{10}$ coefficient just by multiplying out.  
The equality stated in the textbooks holds for the same reason that $1+x+x^2+\dots=\frac{1}{1-x}$. 
