Factoring difference of cubes

Intro Lesson
9:45
Lesson: 1a
3:34
Lesson: 1b
3:00
Lesson: 2a
3:52
Lesson: 2b
2:16
Lesson: 3a
3:08
Lesson: 3b
4:02
Lesson: 4a
3:55
Lesson: 4b
2:44
Lesson: 4c
2:50

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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

,

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

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