Problem

Factor the binomial completely. Use your answers from Exercises as necessary. See Examples...

Factor the binomial completely. Use your answers from Exercises as necessary. See Examples

To help you factor the sum or difference of cubes, complete the following list of cubes.
13 = _________
23 = ________
33 = __________
43 = _______
53 = _________
63 = ________
73 = _________
83 = __________
93 = _______
103 = ________
The following powers of x are all perfect cubes: x3, x6, x9, x12, x15. On the basis of this observation, we may make a conjecture that if the power of a variable is divisible by _________ (with 0 remainder), then we have a perfect cube.

EXAMPLE Factoring Differences of Cubes
Factor each polynomial.
(a) m3 – 125
Let x = m and y = 5 in the pattern for the difference of cubes.
(b) 8p3 – 27
(c) 4m3 – 32
(d) 125t3 − 216s6
EXAMPLE Factoring Sums of Cubes
Factor each polynomial.
(a) k3 + 27
(b) 8m3 + 125n3
(c) 1000a6 + 27b3