### Home > A2C > Chapter 13 > Lesson 13.1.4 > Problem 13-85

13-85.

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 ✎

*x*^{5}+ 8*x*^{2}*y*^{3}8

*y*^{6}− 125*x*^{3}*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.)

*x*^{2}(*x*^{2} + 8*y*^{3})

*x*^{2}(*x* + 2*y*)(*x*^{2} − 2*xy* + 4*y*^{2})

*y*^{6} = (*y*^{2})^{3}

See part (a) for how to factor.

(*x*^{3} + *y*^{3})(*x*^{3} − *y*^{3})

Now factor the sum and difference of the cubes.