how to expand binomials?

sure it is not that difficult.

I'll do it with a semi-specific example

$(a+b)^4= \binom{4}{0} a^4 * b^{0}\;+\;\binom{4}{1} a^3 * b^{1}\;+\;\binom{4}{2} a^2 * b^{2}\;+\; \binom{4}{3} a^1 * b^{3}\;+\;\binom{4}{4} a^0 * b^{4} \\~\\ (a+b)^4=\displaystyle \sum_{n=0}^4\;\;\binom{4}{n}a^{4-n}*b^n$

Do you see the pattern?