Factoring difference of cubes

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  1. 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:

    1. x38x^{3} - 8
    2. x3127x^{3} - \frac{1}{27}
  2. Factoring Using the Difference of Cubes Formula - Extended

    Factor the following expressions:

    1. 27y3127y^{3} - 1
    2. 8x3278x^{3} - 27
  3. Factoring Binomials with 2 variables

    Factor the following expressions:

    1. 27x364y327x^{3} - 64y^{3}
    2. x3y6125x^{3}y^{6} - 125
  4. First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula

    Factor the following expressions:

    1. 16x35416x^{3} - 54
    2. 8x3+1-8x^{3} + 1
    3. 81x43xy381x^{4} - 3xy^{3}
Topic Notes

\bullet Sum of cubes: a3+b3=(a+b)(a2ab+b2)a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

\bullet Difference of cubes: a3b3=(ab)(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)?