Binomial Theorem

 

The Binomial Theorem provides a formula for determining the expansion of a binomial raised to an exponent without having to multiply the terms out by hand. Specifically it says that:

    \[(x + y)^n = \sum_{k=0}^n {n \choose k} x^{n-k}y^k\]

{n \choose k} is called the binomial coefficient and calculated:

{n \choose k} = \dfrac{n!}{k!(n-k)!}

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