Math 45

Sample First Midterm

Dr. Wilson

Problem 8

8. Factor

a3 - b3

This is a difference of cubes. It is best to simply remember the factorization of the difference of cubes. If you don't, you can still figure it out if you remember that one factor is a - b and use long division of polynomials.

and the problem comes out even. Remember that when you are subtracting to change the sign and add. So the difference of cubes factors as

a3 - b3 = (a - b)(a2 + ab + b2)