The coefficient of $x^{20}$ in the expansion of $\left(1+x^2\right)^{40}\left(x^2+2+\frac{1}{x^2}\ri

Question

The coefficient of $x^{20}$ in the expansion of $\left(1+x^2\right)^{40}\left(x^2+2+\frac{1}{x^2}\right)^{-5}$ is

Professor PC Thomas Classes · Answer

$(x^2+2+1/x^2)^{-5} = (x+1/x)^{-10}$. Find coeff of $x^{20}$ in combined expansion yields ${}^{30}C_{25}$.