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

(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 + nxⁿ^–¹a + [n(n–1)/2] xⁿ^–²a² +…+ (ⁿk) xⁿ^–^ka^k + … + aⁿ, where (ⁿk) = n!/(n–k)!k!, the number of combinations of k items selected from n

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

bino′mial the′orem

the theorem giving the expansion of a binomial raised to any power.

[1865–70]

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Noun

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

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References in periodicals archive

According to Google, Khayyam's "Treatise on Demonstration of Problems of Algebra (1070) remains an essential text, introducing the concept of binomial expansion & using conic sections to solve cubic & quadratic equations."

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In fact we can be fairly sure that Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients.

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