Factoring difference of cubes
Factoring difference of cubes
Basic concepts:
 Factor by taking out the greatest common factor
 Factor by grouping
 Factoring difference of squares: $x^2  y^2$
Related concepts:
 Factoring trinomials
 Factoring sum of cubes
Lessons
Notes:
$\bullet$ Sum of cubes: $a^{3} + b^{3} = (a + b)(a^{2}  ab + b^{2})$
$\bullet$ Difference of cubes: $a^{3}  b^{3} = (a  b)(a^{2} + ab + b^{2})$
$\bullet$ SOAP: $a^{3} \pm b^{3} = (a[same sign]b)(a^{2}[opposite sign]ab[always positive]b^{2})$
$\bullet$Things to consider before using the difference of cubes formula:
1. Is there a ‘difference’ sign? Are there two cubed terms?
2. Are the terms in order? (i.e. in descending order of degrees)
3. Is the first term positive?
4. Is there a Greatest Common Factor (GCF)?

2.
Factoring Using the Difference of Cubes Formula
Factor the following expressions:

3.
Factoring Using the Difference of Cubes Formula  Extended
Factor the following expressions:

4.
Factoring Binomials with 2 variables
Factor the following expressions:

5.
First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula
Factor the following expressions: