##  [Multinomial Theorem](/multinomial-theorem) 

  ##  [Multinomial Theorem](https://algebra.quantumdictionary.io/multinomial-theorem-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The generalization of the binomial theorem that expands (x1 + x2 + ... + xm)^n as a sum over all m-tuples of nonnegative integers (k1,...,km) with sum n, with coefficients given by the multinomial coefficients n!/(k1!...km!).