binomial theorem

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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 aibj, such as (a + b)2 = a2 + 2ab + b2.

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 + nxn1a + [n(n–1)/2] xn2a2 +…+ (nk) xnkak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n

bino′mial the′orem


n.
the theorem giving the expansion of a binomial raised to any power.
[1865–70]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.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
References in periodicals archive ?
Milan Pahor introduces and justifies techniques for finding the largest coefficient of binomial expansions.
Then, students are given four or five notebooks, written on various topics such as patterns on binomial expansions and series approximations.
This behaviour is in fact typical of certain binomial expansions and it is a property we exploit to attack larger questions where a direct expansion is impractical.