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 p is a positive integer and x and y 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 x and y differ by 1, say, x = y+1. Then x-y = 1 and
If we also know that then
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