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