Factor. Use your answers in Exercises 1 and 2 as necessary. See Examples 1 and 2.Exercise...

Factor. Use your answers in Exercises 1 and 2 as necessary. See Examples 1 and 2.

Exercise 1

To help factor the sum or difference of cubes, complete the following list of cubes.

13 = _______

23 = _______

33 = _______

43 = _______

53 = _______

63 = _______

73 = _______

83 = _______

93 = _______

103 = _______

Exercise 2

The following powers of x are all perfect cubes: x3, x6, x9, x12, x15. Based on 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 1 Factoring Differences of Cubes

Factor each difference of cubes.

EXAMPLE 2 Factoring Sums of Cubes

Factor each sum of cubes.