Find the constant term in the expansion of $(x^2+1)(x+\frac{1}{x})^{10}$ I can't solve this problem. How to solve it?
The Problem is 
"Find the constant term in the expansion of $
\left({{x}^{2}\mathrm{{+}}{1}}\right){\left({{x}\mathrm{{+}}\frac{1}{x}}\right)}^{\mathrm{10}}
$"

We want to find the coefficients of the binomial expansion of $(x+\frac{1}{x})^{10}$ of the constant term and of the term with $\frac{1}{x^2}$.
$$\left(x+\frac{1}{x}\right)^{10}=\sum_{k=0}^{10}\binom{10}{k}x^{10-k}\frac{1}{x^k}$$
To find the constant term, want $10-k=k$, ie: $k=5$. This term is $\binom{10}{5}x^5\cdot x^{-5}=\binom{10}{5}$. To find the $\frac{1}{x^2}$ term, want $10-2k=2$, ie: $k=4$. Doing the same as above, get that this term is $\binom{10}4 x^{-2}$.
So when you multiply it out, you get that the constant term is $\binom{10}5+\binom{10}4$.
