binomial theorem

American  

noun

Mathematics.

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

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binomial theorem British  

noun

1. 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 + nx ^{n – 1} a + [ n ( n –1)/2] xn ^– ² a ² +…+ ( nk ) xn ^– kak + … + an , where ( nk ) = n !/( n–k )! k !, the number of combinations of k items selected from n

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binomial theorem Scientific  

1. 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 x ^m, the second term is mx ^{m - 1} y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term y ^m is reached. The coefficient of x ^{m - r} is m![r!(m − r)!]. Thus the expansion of (a + b) ³ is a ³ + 3 a ² b + 3 ab ² + b ³.

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Etymology

Origin of binomial theorem

First recorded in 1865–70

Example Sentences

See Examples For:

binomial theorem

Published last week in Philadelphia was a convenient 236-page treatise, Algebra for Parents* calculated to save elders considerable embarrassment when asked to explain anything from simple addition to the binomial theorem.

From Time Magazine Archive

Well," drawled Publicist Bernays, "there are two other young men here and we were just discussing the binomial theorem.

From Time Magazine Archive

At any rate, the mixture of science and religion is curious, as if Billy Sunday had undertaken a sermon on the subject of the binomial theorem.

From Time Magazine Archive

It never seems to occur to the teacher that the pupil of the third grade might give the words of the binomial theorem without the slightest apprehension of its meaning.

From The Vitalized School by Pearson, Francis B.

The courtships are varied between abrupt embraces soon after introduction, and discussions on Hebrew, Babel, "Christian-deism," and the binomial theorem.

From The English Novel by Saintsbury, George