The binomial theorem states that where $n$ is an integer $$(x+y)^n=\sum_{k=0}^n\binom nkx^ky^{n-k}$$ where the binomial coefficient $\binom nk=\frac{n!}{k! (n - k)!}$
This can be extended as the binomial series, an infinite series representation for functions of the form $(1 + x)^{\alpha}$, where $\alpha$ is an arbitrary complex number.