Lesson 7 – Factoring a Sum or Difference of Cubes
Sum of Cubes
An expression that contains two perfect cubes added together can be factored as follows:
𝐴3 + 𝐵3 = (𝐴 + 𝐵)(𝐴2 − 𝐴𝐵 + 𝐵2 )
Note:
3
√𝐴3 = 𝐴
Difference of Cubes
An expression that contains perfect cubes where one is subtracted from the other can be factored as
follows:
𝐴3 − 𝐵3 = (𝐴 − 𝐵)(𝐴2 + 𝐴𝐵 + 𝐵2 )
Example 1:
Example 2:
Prove the Sum of Cubes Formula using the factor theorem.
Factor each of the following:
a) 8𝑥 3 + 64
c) 125(𝑥 − 8)3 + 8(2𝑥 + 1)3
b) 𝑥 9 − 1