# binomial theorem

binomial theorem

**MLA Style**

"binomial theorem." YourDictionary, n.d. Web. 09 November 2018. <https://www.yourdictionary.com/binomial-theorem>.

**APA Style**

binomial theorem. (n.d.). Retrieved November 09th, 2018, from https://www.yourdictionary.com/binomial-theorem

## binomial theorem

noun

*Mathematics*

*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}.

**MLA Style**

"binomial theorem." YourDictionary, n.d. Web. 09 November 2018. <https://www.yourdictionary.com/binomial-theorem>.

**APA Style**

binomial theorem. (n.d.). Retrieved November 09th, 2018, from https://www.yourdictionary.com/binomial-theorem

Mathematics

*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}.

**MLA Style**

"binomial theorem." YourDictionary, n.d. Web. 09 November 2018. <https://www.yourdictionary.com/binomial-theorem>.

**APA Style**

binomial theorem. (n.d.). Retrieved November 09th, 2018, from https://www.yourdictionary.com/binomial-theorem

**MLA Style**

**APA Style**