Algebra
Intermediate

Binomial Theorem

Expands any power of a binomial into a sum of terms.

Formula

(a+b)n=∑k=0n(nk)an−kbk(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

Variables

a, bTerms of the binomial
nPower (non-negative integer)

Example

(x+1)³ = x³ + 3x² + 3x + 1

Did You Know?

The coefficients form Pascal's Triangle, known in Persia, China, and India centuries before Pascal was born.

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