# Factoring sum of cubes

### Factoring sum of cubes

#### Lessons

$\bullet$ 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)?

• Introduction
Introduction to factoring sum of cubes

i. What is sum of cubes?

ii. How can sum of cubes be factored?

• 1.
Factoring Using the Sum of Cubes Formula

Factor the following expressions:

a)
$x^{3} + 125$

b)
$x^{3} + \frac{8}{27}$

• 2.
Factoring Using the Sum of Cubes Formula - Extended

Factor the following expressions:

a)
$64x^{3} + 1$

b)
$125x^{6} + 8$

• 3.
Factoring Binomials with 2 variables

Factor the following expressions:

a)
$8x^{6} + 27y^{9}$

b)
$x^{12}y^{6} + 64$

• 4.
First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula

Factor the following expressions:

a)
$-x^{3} - 8$

b)
$54x^{3} + 128$

c)
$81x^{10}y + 24xy^{7}$

• 5.
Making a Conclusion on Factoring Binomials

Overview – Factoring Binomials

i. How to identify which formulas to use?

ii. What are the aspects we need to consider before factoring?