3.6 Pascal’s Triangle and the Binomial Theorem

Counting

Binomial Theorem

• If $n$ is a non-negative integer, then

$$(x+y{)}^n=(\genfrac{}{}{0ex}{}{n}{0})x^n+(\genfrac{}{}{0ex}{}{n}{1})x^{n-1}y+(\genfrac{}{}{0ex}{}{n}{2})x^{n-2}{y}^2+(\genfrac{}{}{0ex}{}{n}{3})x^{n-3}{y}^3+\cdots +(\genfrac{}{}{0ex}{}{n}{n-1})x{y}^{n-1}+(\genfrac{}{}{0ex}{}{n}{n})y^n.$$