binomial theorem

The binomial theoremMathworldPlanetmath is a formulaMathworldPlanetmathPlanetmath for the expansion of (a+b)n, for n a positive integer and a and b any two real (or complex) numbers, into a sum of powers of a and b. More precisely,


For example, if n is 3 or 4, we have:

(a+b)3 =a3+3a2b+3ab2+b3
(a+b)4 =a4+4a3b+6a2b2+4ab3+b4.

This result actually holds more generally if a and b belong to a commutativePlanetmathPlanetmathPlanetmath rig (

Title binomial theorem
Canonical name BinomialTheorem
Date of creation 2013-03-22 11:46:47
Last modified on 2013-03-22 11:46:47
Owner KimJ (5)
Last modified by KimJ (5)
Numerical id 17
Author KimJ (5)
Entry type Theorem
Classification msc 11B65
Classification msc 06F25
Classification msc 03E20
Related topic BinomialFormula
Related topic BinomialCoefficient
Related topic BernoulliDistribution2
Related topic UsingThePrimitiveElementOfBiquadraticField