二项式定理
Also known as Al-Karaji-newton theorem
algebraic expansion of powers of a binomial
AI overview
The binomial theorem is a mathematical formula that tells you how to expand expressions like (a + b)^n into a sum of simpler terms without having to multiply them out manually. It matters because it's a foundational tool in algebra and higher mathematics that saves time in calculations and helps solve problems in probability, statistics, and many other fields.
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Article · 中文
二项式定理（英語：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展开为类似项之和的恒等式，其中、均为非负整数且。系数是依赖于和的正整数。当某项的指数为1时，通常略去不写。例如： 中的系数被称为二项式系数，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。
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