English Dictionary

binomial theorem

名詞

(mathematics) A formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example:

日本語の意味

数学において、二項定理とは、(a+b)のn乗（nは正の整数）の展開を求める定理であり、(a+b)ⁿをaとbのべき乗の積の形で表される各項の加算式に展開する公式である。

The binomial theorem lets us expand (a+b)n into a sum of terms whose coefficients are positive integers.

二項定理を使うと、(a+b)^n を各項の係数が正の整数である項の和として展開できます。

意味（1）

(mathematics) A formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example:

(x+y)⁴;=;x⁴,+,4x³ʸ,+,6x²y²,+,4xy³,+,y⁴.