${\displaystyle (a+b{)}^n=\sum _{r=0}^n\left(\begin{array}{c}n\\ r\end{array}\right).a^{n-r}.b^r}$

or

$(a+b{)}^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right).a^{n-1}.b+\left(\begin{array}{c}n\\ 2\end{array}\right).a^{n-2}.b^2+\left(\begin{array}{c}n\\ 3\end{array}\right).a^{n-3}.b^3+\dots +b^n$