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.

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