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 3b 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 6y 6

First, notice that x 6y 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.

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