# binomial theorem

## binomial theorem

*noun*

## Definition of *BINOMIAL THEOREM*

**:**a theorem that specifies the expansion of a binomial of the form (

*x + y*) to the exponent

*n*as the sum of

*n*+ 1 terms of which the general term consists of a product of

*x*and

*y*with

*x*raised to the exponent (

*n - k*) and

*y*raised to the exponent

*k*and a coefficient consisting of n! divided by (

*n - k*)!

*k*! where

*k*takes on values from 0 to

*n*

## First Known Use of *BINOMIAL THEOREM*

## binomial theorem

*noun*

*(Concise Encyclopedia)*

In algebra, a formula for expansion of the binomial (*x* + *y*) raised to any positive integer power. A simple case is the expansion of (*x* + *y*)^{2}, which is *x*^{2} + 2*x**y* + *y*^{2}. In general, the expression (*x* + *y*)^{n} expands to the sum of (*n* + 1) terms in which the power of *x* decreases from *n* to 0 while the power of *y* increases from 0 to *n* in successive terms. The terms can be represented in factorial notation by the expression [*n*!/(*n* *r*)!*r*!)]*x*^{n r}*y*^{r} in which *r* takes on integer values from 0 to *n*.

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