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

1753

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 x² + 2xy + y². 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.