Задача 9.

(Binomial expansion) 1) Open the parentheses in the following expressions $(a+b)$, $(a+b)^2$, $(a+b)^3$, $(a+b)^4$ and write down the results one under the other. Note that the coefficients form Pascal's triangle. 2) Show that \begin{equation*} (a+b)^n = \binom{n}{0}a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{n}b^n. \end{equation*}.