# 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,

For example,

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

.

For example,

If we also know that then

## See Also

- Factoring
- Difference of squares, an extremely common specific case of this.

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