The expansion of any non-negative integer power n of the binomial x + y is a sum of the form
$$(x + y)^n = \binom{n}{0} x^n y^0 + \binom{n}{1} x^{n - 1} y^1 + \binom{n}{2} x^{n - 2} y^2 + \cdots + \binom{n}{n} x^0 y^n,$$
where each $\binom{n}{k}$ is a positive integer known as a binomial coefficient, defined as
$$ \begin{align} \binom{n}{k} &= \frac{n!}{k! (n - k)!} \\ &= \frac{n (n - 1) (n - 2) \cdots (n - k + 1)}{k (k - 1) (k - 2) \cdots 2 \cdot 1} \end{align} $$
This formula is also referred to as the binomial formula or the binomial identity.
Using summation notation, it can be written more concisely as
$$(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k = \sum_{k=0}^{n} \binom{n}{k} x^k y^{n - k}$$