How to factor Difference of Cubes

Formula for difference of cubes and their factors

The general formula for the factors of the difference of cubes is

a³ − b³ = (a − b)(a² + ab + b²)

How to factor difference of cubes

In order to understand how to factor the difference of cubes, we will follow the same approach as we did with the sum of cubes. Let's start with two factors whose product is difference of cubes. This approach of starting from the factors will help explain the formula for the difference of cubes.

(x − 3) (x² + 3x + 9)
- x³ + 3x² + 9x
- + –3x² –9x – 27
- x³ + 3x² – 3x² + 9x –9x – 27 (Notice the terms that cancel out)
- x³– 27 = x³ – 3³

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