Factoring difference of cubes

Factoring difference 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 difference of cubes

i. What is difference of cubes?

ii. How can difference of cubes be factored?

• 1.
Factoring Using the Difference of Cubes Formula

Factor the following expressions:

a)
$x^{3} - 8$

b)
$x^{3} - \frac{1}{27}$

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

Factor the following expressions:

a)
$27y^{3} - 1$

b)
$8x^{3} - 27$

• 3.
Factoring Binomials with 2 variables

Factor the following expressions:

a)
$27x^{3} - 64y^{3}$

b)
$x^{3}y^{6} - 125$

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

Factor the following expressions:

a)
$16x^{3} - 54$

b)
$-8x^{3} + 1$

c)
$81x^{4} - 3xy^{3}$