binomial theorem

noun Mathematics.

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

Nearby words

  1. binomial coefficient,
  2. binomial distribution,
  3. binomial experiment,
  4. binomial nomenclature,
  5. binomial series,
  6. binominal,
  7. binormal,
  8. binotic,
  9. binovular,
  10. binoxalate

Origin of binomial theorem

First recorded in 1865–70 Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

British Dictionary definitions for binomial theorem

binomial theorem


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 = x n + nx n 1 a + [ n (n –1)/2] x n ² a ² +…+ (n k) x n k a k + … + a n, where (n k) = n !/(n–k)! k !, the number of combinations of k items selected from n
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Science definitions for binomial theorem

binomial theorem


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.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.