### Home > CCA2 > Chapter 12 > Lesson 12.1.4 > Problem12-73

12-73.

Parts (a) through (d) of problem 12-72 represent a general pattern known as the sum and difference of cubes. Use this pattern to factor each of the following polynomials.

The sum and difference of cubes formulas are:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

1. $x^3 + y^3$

Factor using the sum of cubes formula.

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

2. $x^3 - 27$

$\text{27 is } 3^3.$

$(x - 3)(x^2 + 3x + 9)$

3. $8x^3 − y^3$

$\text{Rewrite the polynomial as}\ (2x)^3 - y^3.$

Now factor using the difference of cubes formula.

4. $x^3 + 1$

$\text{Rewrite the polynomial as } x^3 + 1^3.$

Now factor using the sum of cubes formula.

5. Make up another problem involving the sum or difference of cubes and show how to factor it.