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# Binomial theorem

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

International Congress of Arts and Science, Volume I Various
The Eulogy of Richard Jefferies Walter Besant
Memoirs of Sherlock Holmes Sir Arthur Conan Doyle
A Review of Algebra Romeyn Henry Rivenburg
Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5 Various
Soul of a Bishop H. G. Wells
The Theory of the Theatre Clayton Hamilton
Mrs. Warren’s Daughter Sir Harry Johnston
Studies in Logical Theory John Dewey
The Life of the Fly J. Henri Fabre

noun
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–kak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n
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 xm, the second term is mxm-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 ym is reached. The coefficient of xm-r is m![r!(m-r)!]. Thus the expansion of (a + b)3 is a3 + 3a2b + 3ab2 + b3.

Tagged:

• Binomial-nomenclature

a system of nomenclature in which each species is given a unique name that consists of a generic and a specific term. noun a system for naming plants and animals by means of two Latin names: the first indicating the genus and the second the species to which the organism belongs, as in Panthera leo […]

• Binominal name

noun Examples

• Binominal

adjective of or denoting the binomial nomenclature noun a two-part taxonomic name; binomial Historical Examples The Systematics of the Frogs of the Hyla Rubra Group in Middle America Juan R. Len

• Binos

binos binoculars Historical Examples The Jesuit Relations and Allied Documents, Vol. I: Acadia, 1610-1613 Various A History of Inventions, Discoveries, and Origins, Volume I (of 2) Johann Beckman

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