Combinatorics/Binomial Theorem

The Binomial Theorem

The Binomial Theorem determines the expansion for the powers of different sums; written out, it is:

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

Here, $(\binom{n}{i}) = \frac{n!}{i! (n - i)!}$ is the combination of n and i.

Thus, $(x + 2)^{2} = 1 x^{2} + 2 x^{1} 2^{1} + 2^{2} = x^{2} + 4 x + 4$

and $(x + y)^{5} = x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}$

Combinatorics/Binomial Theorem

The Binomial Theorem

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