# Factoring difference of cubes

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##### Introduction
###### Lessons
1. Introduction to Factoring difference of cubes

i. What is difference of cubes?

ii. How can difference of cubes be factored?

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##### Examples
###### Lessons
1. Factoring Using the Difference of Cubes Formula

Factor the following expressions:

1. $x^{3} - 8$
2. $x^{3} - \frac{1}{27}$
2. Factoring Using the Difference of Cubes Formula - Extended

Factor the following expressions:

1. $27y^{3} - 1$
2. $8x^{3} - 27$
3. Factoring Binomials with 2 variables

Factor the following expressions:

1. $27x^{3} - 64y^{3}$
2. $x^{3}y^{6} - 125$
4. First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula

Factor the following expressions:

1. $16x^{3} - 54$
2. $-8x^{3} + 1$
3. $81x^{4} - 3xy^{3}$
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###### Topic 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)?