# binomial theorem

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Related to binomial theorem: binomial distribution, Binomial coefficient, Pascal's triangle, Binomial expansion

## binomial theorem

*n.*

*Mathematics*

The theorem that specifies the expansion of any power (

*a*+*b*)*of a binomial (*^{m}*a*+*b*) as a certain sum of products*a*, such as (^{i}b^{j}*a*+*b*)^{2}=*a*^{2}+ 2*ab*+*b*^{2}.American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## binomial theorem

*n*

(Mathematics) 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*, where (^{n}*) =*^{n}k*n*!/(*n–k*)!*k*!, the number of combinations of*k*items selected from*n*Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## bino′mial the′orem

*n.*

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

[1865–70]

Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.

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Noun | 1. | binomial theorem - a theorem giving the expansion of a binomial raised to a given powerstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters probability theory, theory of probability - the branch of applied mathematics that deals with probabilities theorem - a proposition deducible from basic postulates |

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