Sum and difference of powers
The sum and difference of powers are powerful factoring techniques that, respectively, factor a sum or a difference of certain powers.
Sums of Powers
Differences of Powers
If is a positive integer and and are real numbers,
Note that the number of terms in the long factor is equal to the exponent in the expression being factored.
An amazing thing happens when and differ by , say, . Then and
If we also know that then:
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