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 = xn + nxn–1a + [n(n–1)/2] xn–2a2 +…+ (nk) xn–kak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n