Coefficient of product of polynomials. Suppose we have the polynomial $f(x)$ and another polynomial $g(x)$. How can I find the coefficient of say $x^n$ in the product of the polynomials without actually multiplying. I am not that experienced with $n$ choose $k$. You can take  specific polynomials, I'm just trying to understand and gain more math skills. Thanks.

$$\begin{cases}f(x)=a_nx^n+a_{n-1}x^{n-1}+....+a_1x+a_0\\g(x)=b_mx^m+b_{m-1}x^{m-1}+....+b_1x+b_0\end{cases}$$
$$f(x)g(x)=\sum_{k=0}^{m+n}c_kx^k$$ and $$c_k=\sum_{i+j=k}a_ib_j$$
See the coefficients $c_0$ and $c_1$ and $c_2$. It is easy to verify
