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binomial theorem

noun, Mathematics
the theorem giving the expansion of a binomial raised to any power.
1865-70 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the web for binomial theorem
  • Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion.
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 = xn + nxn1a + [n(n–1)/2] xn²a² +…+ (nk) xnkak + … + an, where (nk) = 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
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binomial theorem in Science
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 © 2002. Published by Houghton Mifflin. All rights reserved.
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