Lesson 6 – Factoring a Sum or Difference of Cubes
Ex. 1 Factor: 𝑓(𝑥) = 𝑥 3 − 8
Sum of Cubes
An expression that contains two perfect cubes added together can be factored as follows:
𝐴3 + 𝐵 3 = (𝐴 + 𝐵)(𝐴2 − 𝐴𝐵 + 𝐵 2 )
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 − 𝐵 3 = (𝐴 − 𝐵)(𝐴2 + 𝐴𝐵 + 𝐵 2 )
Example 2:
a) 𝑥 3 + 125
Factor each of the following:
b) 27𝑥 3 − 64
Ex. 3
Factor fully.
a) 𝑥 4 + 8𝑥
c) 𝑥 3 − 8(𝑥 + 1)3
HW: p.182 #2bdg, 3, 5
b) 𝑥 9 − 1