binomial theorem science definition

The theorem that specifies the expansion of any power of a binomial, that is, (a + b)^m. According to the binomial theorem, the first term of the expansion is x^m, the second term is mx^m-1y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term y^m is reached. The coefficient of x^m-r is m![r!(m-r)!]. Thus the expansion of (a + b)³ is a³ + 3a²b + 3ab² + b³.