Binomial Theorem

The expansion of a binomial $(x+y)$ to a power $n$ can be written as sum using the Binomial formula of the binomial Theorem.

$$(x+y{)}^n=\sum \_{k=0}^n(\frac{n}{k})x^{n-k}{y}^k=\sum \_{k=0}^n(\frac{n}{k})x^k{y}^{n-k}$$

Where each $(\frac{n}{k})$ is a positive integer known as binomial coefficient, defined as

$$(\frac{n}{k})=\frac{n!}{k!(n-k)!}$$