Tutoring high school math, you rarely see this; it comes up often, however, in calculus.  The tutor offers a light treatment.

How do you factor x^3 + 125? You need the following formula:

a^3 + b^3 = (a + b)(a^2 – ab + b^2)

Of course, 125=5^3. Carefully substituting x for a and 5 for b, we arrive at

x^3 + 125=(x+5)(x^2-5x+25)

What about factoring 8x^3+1?

We need to realize that, really,

8x^3+1=(2x)^3 + 1^3

Substituting 2x for a and 1 for b in the formula, we arrive at

8x^3+1=(2x+1)((2x)^2 – 2x(1) + 1^2)=(2x+1)(4x^2 – 2x + 1)

For a hint about factoring the difference of cubes, please come back soon:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.