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# Binomial theorem

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 $(x + y)^n = \sum_{k=0}^n \binom n k x^{n-k} y^{k}$