Sum or Difference of Cubes

A polynomial in the form a³ + b³ is called a sum of cubes. A polynomial in the form a³ − b³ is called a difference of cubes.

Both of these polynomials have similar factored patterns:

• A sum of cubes:
  

  
  

A difference of cubes:

Example 1: Factor x³ + 125.

Example 2: Factor 8 x³ − 27.

Example 3: Factor 2 x³ + 128 y³.

First find the GFC. GFC = 2

Example 4: Factor x⁶ − y⁶.

First, notice that x⁶ − y⁶ is both a difference of squares and a difference of cubes.

In general, factor a difference of squares before factoring a difference of cubes.

Cite this article