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. x3−8x^{3} - 8
    2. x3−127x^{3} - \frac{1}{27}
  2. Factoring Using the Difference of Cubes Formula - Extended

    Factor the following expressions:

    1. 27y3−127y^{3} - 1
    2. 8x3−278x^{3} - 27
  3. Factoring Binomials with 2 variables

    Factor the following expressions:

    1. 27x3−64y327x^{3} - 64y^{3}
    2. x3y6−125x^{3}y^{6} - 125
  4. First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula

    Factor the following expressions:

    1. 16x3−5416x^{3} - 54
    2. −8x3+1-8x^{3} + 1
    3. 81x4−3xy381x^{4} - 3xy^{3}
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Topic Notes

∙\bullet Sum of cubes: a3+b3=(a+b)(a2−ab+b2)a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

∙\bullet Difference of cubes: a3−b3=(a−b)(a2+ab+b2)a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})

∙\bullet SOAP: a3±b3=(a[samesign]b)(a2[oppositesign]ab[alwayspositive]b2)a^{3} \pm b^{3} = (a[same sign]b)(a^{2}[opposite sign]ab[always positive]b^{2})

∙\bulletThings 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)?

Basic Concepts
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