### Definition of Binomial theorem

1. Noun. A theorem giving the expansion of a binomial raised to a given power.

Category relationships: Statistics
Group relationships: Probability Theory, Theory Of Probability
Generic synonyms: Theorem

### Definition of Binomial theorem

1. Noun. (mathematics) A formula giving the expansion of a binomial such as $\left( a + b \right)$ raised to any positive integer power, i.e. $\left( a + b \right)^\left\{n\right\}$. It's possible to expand the power into a sum of terms of the form $ax^\left\{b\right\}y^\left\{c\right\}$ where the coefficient of each term is a positive integer. For example: ¹

¹ Source: wiktionary.com

### Binomial Theorem Pictures

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### Lexicographical Neighbors of Binomial Theorem

 binocularitiesbinocularitybinocularlybinocularsbinoculatebinodalbinomenbinomialbinomial coefficientbinomial coefficients binomial distributionbinomial distributionsbinomial namebinomial namesbinomial nomenclaturebinomial theorem (current term)binomiallybinomialsbinominabinominal binominal namebinominalsbinominousbinormalbinosbinospironebinoticbinousbinoxalatebinoxalates

### Literary usage of Binomial theorem

Below you will find example usage of this term as found in modern and/or classical literature:

1. Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools by George Chrystal (1893)
"Using the expressions just found for nCM nC,, &c., we now have This is the Binomial Theorem as Newton discovered it, proved, of course, as yet for positive ..."

2. College Algebra by Webster Wells (1890)
"THE binomial theorem. POSITIVE INTEGRAL EXPONENT. 442. The. binomial theorem is a formula by means of which any power of a binomial may be 'expanded into a ..."

3. Elements of the Differential and Integral Calculus: With Examples and by James Morford Taylor, William Christ (1889)
"... deduce the binomial theorem. Here /( x + y) = (x /'"(«)= m(m — 1) (т — 2) ж"-*, etc. Substituting these values in Taylor's formula, we have (x ~ t 90. ..."

4. Abstracts of the Papers Printed in the Philosophical Transactions of the by Royal Society (Great Britain) (1833)
"Note respecting the Demonstration of the binomial theorem inserted in the last Volume of the Philosophical Transactions. By Thomas Knight, Esq. Communicated ..."

5. The Collected Mathematical Papers of Arthur Cayley by Arthur Cayley (1889)
"NOTE ON A GENERALIZATION OF A binomial theorem. [From the Philosophical Magazine, vol. vi. (1853), p. 185.] THE formula (Grelle, ti [1826] p. ..."

6. College Algebra by James Harrington Boyd (1901)
"Particular cases of the binomial theorem can be found by multiplication. ... The results arrived at in 1-5 constitute as a whole the binomial theorem. ..."