Sum or Difference of Cubes
A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 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 x 3 + 125.
Example 2
Factor 8 x 3 – 27.
Example 3
Factor 2 x 3 + 128 y 3.
First find the GCF. GCF = 2 
Example 4
Factor x 6 – y 6.
First, notice that x 6 – y 6 is both a difference of squares and a difference of cubes.
In general, factor a difference of squares before factoring a difference of cubes.
