British Dictionary definitions for binomial theorem

binomial theorem

noun

a mathematical theorem that gives the expansion of any binomial raised to a positive integral power, n . It contains n + 1 terms: (x + a) n = x n + nxn–1a + [ n (n –1)/2] x n– ² a ² +…+ (nk) x n–k a k + … + a n, where (nk) = n !/(n–k)! k !, the number of combinations of k items selected from n

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 xm, the second term is mxm-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 ym is reached. The coefficient of xm-r is m![r!(m-r)!]. Thus the expansion of (a + b)3 is a3 + 3a2b + 3ab2 + b3.