# 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: b

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