Factoring Special Patterns

Sum & Difference of Cubes

If you have a cubic polynomial that is the sum or difference of two perfect cubes, the following special products can be used to factor the polynomial:

Sum of Cubes:x³ + y³ = (x + y) (x² - xy + y²)

Difference of Cubes:x³ - y³ = (x - y) (x² + xy + y²)

Example Factor the following polynomial: 64x³ + 125.

Step 1. Determine if you have a sum or difference of two cubes.

64x³ is (4x)³ and 125 is 5³, so this is a sum of cubes.

Step 2. Use the pattern to factor.

(x + y) (x² - xy + y²); x = 4x and y = 5

Sum&Difference1

*Note: Using Distributive Property to multiply the two terms will verify the polynomial was factored completely.

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