### Home > CCA2 > Chapter 12 > Lesson 12.1.4 > Problem12-79

12-79.

Use the sum or difference of cubes and what you already know about factoring to factor the following expressions as completely as possible. Homework Help ✎

Refer to problem 12-73 for the patterns of sums and differences of cubes.

1. $x^5 + 8x^2y^3$

Notice that $x^2$ is a common factor for both terms.
Factor it out. Then use the sum of cubes to factor it completely.
Recall that $8 = 2^3$.

1. $8y^6 - 125x^3$

This is already in the form you need.
Use the difference of cubes to factor it.
What are the cubes?

1. $x^6 - y^6$ (Note: This is tricky. If you start it as the difference of two cubes, you will not be able to factor it completely. Think of it as the difference of two squares and then factor the factors as the sum and difference of two cubes.)

$\left(x^3\right)^2-\left(y^3\right)^2$

$(x + y)(x^2 - 2xy + y^2)(x - y)(x^2 + 2xy + y^2)$