Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Common Products and Factors

常见产品和因数

Any power of a binomial can be obtained from the Binomial Theorem.

任何二项式的幂都可以通过二项式定理获得。

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Binomial Theorem

二项式定理

For any value of n, whether positive, negative, integer or non-integer, the value of the nth power of a binomial is given by:

对于任何值的n,无论是正数、负数、整数还是非整数,二项式的n次幂的值由以下公式给出:

There are many binomial expansion applications in physics.

物理学中有很多二项式展开的应用
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Binomial Expansion

二项式展开

For any power of n, the binomial (a + x) can be expanded

对于任何n的幂,二项式(a + x)可以展开


This is particularly useful when x is very much less than a so that the first few terms provide a good approximation of the value of the expression. There will always be n+1 terms and the general form is:

这在x远小于a时特别有用,此时前几项可以很好地近似表达式的值。无论何时,总共有n+1项,一般形式为:

** Examples
示例

Applications

应用
Kinematic time dilation
运动时间膨胀
Gravitational time dilation
引力时间膨胀
Kinetic energy
动能
Electric quadrupole field
电四极场
Relativity factor gamma
相对论因子伽马
...
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Binomial Expansion Examples

二项式展开示例

The binomial expansion is a useful example of a series. Some common examples of its application are:

二项式展开是一个有用的级数例子。其一些常见应用包括:


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