The binomial theorem describes the algebraic expansion of powers of a binomial.
If we let \(x\) and \(y\) be variables and \(n\) is a non-negative integer. The expansion of \((x+y)^n\) can be formalised as \[ (x + y)^n = \sum_{k=0}^n \binom n k x^k y^{n-k} \] where \(\binom n k\) is each Binomial coefficient.
This may equivalently be expressed as \[ (x + y)^n = \sum_{k=0}^n \binom n k x^{n-k} y^{k} \]