# 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:
 Noun 1 binomial theorem - a theorem giving the expansion of a binomial raised to a given powerstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parametersprobability theory, theory of probability - the branch of applied mathematics that deals with probabilitiestheorem - a proposition deducible from basic postulates
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The topics include the multiplication principle, the distribution of balls into boxes, the binomial expansion, the principles of inclusion and exclusion, the pigeonhole principle, and the Catalan numbers.
jkRo], binomial expansion may be used to obtain a series representation, and the approximate expression is