Factoring sum of cubes

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Introduction to factoring sum of cubes
i. What is sum of cubes?

ii. How can sum of cubes be factored?

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Factoring Using the Sum of Cubes Formula
Factor the following expressions:
1. $x^{3} + 125$
2. $x^{3} + \frac{8}{27}$
Factoring Using the Sum of Cubes Formula - Extended
Factor the following expressions:
1. $64x^{3} + 1$
2. $125x^{6} + 8$
Factoring Binomials with 2 variables
Factor the following expressions:
1. $8x^{6} + 27y^{9}$
2. $x^{12}y^{6} + 64$
First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula
Factor the following expressions:
1. $-x^{3} - 8$
2. $54x^{3} + 128$
3. $81x^{10}y + 24xy^{7}$
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?

$\bullet$ 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)?