binomial theorem

WordReference Random House Unabridged Dictionary of American English © 2025

bino′mial the′orem, [Math.]

1. Mathematics the theorem giving the expansion of a binomial raised to any power.

• 1865–70

Collins Concise English Dictionary © HarperCollins Publishers::

binomial theorem noun

1. 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 + nx^n–1a + [n(n–1)/2] x^n–2a² +…+ (ⁿ_k) x^n–ka^k + … + aⁿ, where (ⁿ_k) = n!/(n–k)!k!, the number of combinations of k items selected from n