binomial theorem

noun

Mathematics.

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

binomial theorem

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

binomial theorem

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.

Word History and Origins

Origin of binomial theorem¹

First recorded in 1865–70

Example Sentences

Given his obsession with the binomial theorem, we based the code we created for him on Pascal’s triangle.

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Expand by the binomial theorem and simplify: 8.

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The binomial theorem operates irrespective of the values substituted for its symbols.

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Later still he made what seemed to be approaches toward Newton’s binomial theorem.

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Expand each term by the binomial theorem, and let us fix our attention on the coefficient of yn−1.

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