the general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b): discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b) = a + 2ab + b)

# binomial theorem

binomial theoremWebster's New World College Dictionary, Fifth Edition Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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"Binomial theorem."

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*YourDictionary*. Retrieved from https://www.yourdictionary.com/binomial-theorem## binomial theorem

noun

*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}.THE AMERICAN HERITAGE® DICTIONARY OF THE ENGLISH LANGUAGE, FIFTH EDITION by the Editors of the American Heritage Dictionaries. Copyright © 2016, 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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**MLA Style**

"Binomial theorem."

*YourDictionary*. LoveToKnow. www.yourdictionary.com/binomial-theorem.**APA Style**

Binomial theorem. (n.d.). In

*YourDictionary*. Retrieved from https://www.yourdictionary.com/binomial-theorem

Mathematics

The theorem that specifies the expansion of any power of a binomial, that is, (

*a*+*b*)*According to the binomial theorem, the first term of the expansion is*^{m}.*x*, the second term is^{m}*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*is reached. The coefficient of^{m}*x*is^{m-r}*m*![*r*!(*m*−*r*)!]. Thus the expansion of (*a*+*b*)^{3}is*a*^{3}+ 3*a*^{2}*b*+ 3*ab*^{2}+*b*^{3}.Link to this page

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**MLA Style**

"Binomial theorem."

*YourDictionary*. LoveToKnow. www.yourdictionary.com/binomial-theorem.**APA Style**

Binomial theorem. (n.d.). In

*YourDictionary*. Retrieved from https://www.yourdictionary.com/binomial-theoremEnglish Wiktionary. Available under CC-BY-SA license.

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**MLA Style**

"Binomial theorem."

*YourDictionary*. LoveToKnow. www.yourdictionary.com/binomial-theorem.**APA Style**

*YourDictionary*. Retrieved from https://www.yourdictionary.com/binomial-theorem