在初等代数中，二项式定理（英语：Binomial theorem）描述了二项式的幂的代数展开。根据该定理，可以将两个数之和的整数次幂诸如(x + y) 展开为类似 axy 项之和的恒等式，其中b、c均为非负整数且b + c = n。系数a是依赖于n和b的正整数。当某项的指数为0时，通常略去不写。例如：

axy 中的系数a被称为二项式系数，记作 或 （二者值相等）。二项式定理可以推广到任意实数次幂，即广义二项式定理。

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y) into a sum involving terms of the form a x y, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example,