binomial theorem

binomial theorem

n. Mathematics

The theorem that specifies the expansion of any power (a + b)^m of a binomial (a + b) as a certain sum of products aⁱb^j, such as (a + b)² = a² + 2ab + b².

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binomial theorem

n

(Mathematics) a mathematical theorem that gives the expansion of any binomial raised to a positive integral power, n. It contains n + 1 terms: (x + a)ⁿ = xⁿ + nx^n-1 a + [n(n-1)/2] x^n-2a² +…+ (ⁿ_k) x^n-ka^k + … + aⁿ, where (ⁿ_k) = n!/(n-k)!k!, the number of combinations of k items selected from n

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binomial theorem

Mathematics

The theorem that specifies the expansion of any power of a binomial, that is, (a + b)^m. According to the binomial theorem, the first term of the expansion is x^m, the second term is mx^m-1y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term y^m is reached. The coefficient of x^m-r is m![r!(m-r)!]. Thus the expansion of (a + b)³ is a³ + 3a²b + 3ab² + b³.

Thesaurus

Noun

1.

binomial theorem - a theorem giving the expansion of a binomial raised to a given power statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters probability theory, theory of probability - the branch of applied mathematics that deals with probabilities theorem - a proposition deducible from basic postulates