Binomial Theorem Definition

noun
The theorem that specifies the expansion of any power ( a + b ) m of a binomial ( a + b ) as a certain sum of products aibj , such as ( a + b )2 = a2 + 2 ab + b2 .
American Heritage
The general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b)n: discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b)2 = a2 + 2ab + b2)
Webster's New World

(mathematics) A formula giving the expansion of a binomial such as raised to any positive integer power, i.e. . It's possible to expand the power into a sum of terms of the form where the coefficient of each term is a positive integer. For example.

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