binomial theorem Mathematics 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-1}y, 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 a^{3} + 3a^{2}b + 3ab^{2} + b^{3}. |