Common Products and Factors

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

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Binomial Theorem

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

There are many binomial expansion applications in physics.

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Binomial Expansion

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



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:


**Examples

Applications

Kinematic time dilationGravitational time dilation
Kinetic energyElectric quadrupole field
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Binomial Expansion Examples

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



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