Factoring difference of cubes

Factoring difference of cubes

Lessons

\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)?

  • 1.
    Introduction to Factoring difference of cubes

    i. What is difference of cubes?

    ii. How can difference of cubes be factored?


  • 2.
    Factoring Using the Difference of Cubes Formula

    Factor the following expressions:

    a)
    x38x^{3} - 8

    b)
    x3127x^{3} - \frac{1}{27}


  • 3.
    Factoring Using the Difference of Cubes Formula - Extended

    Factor the following expressions:

    a)
    27y3127y^{3} - 1

    b)
    8x3278x^{3} - 27


  • 4.
    Factoring Binomials with 2 variables

    Factor the following expressions:

    a)
    27x364y327x^{3} - 64y^{3}

    b)
    x3y6125x^{3}y^{6} - 125


  • 5.
    First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula

    Factor the following expressions:

    a)
    16x35416x^{3} - 54

    b)
    8x3+1-8x^{3} + 1

    c)
    81x43xy381x^{4} - 3xy^{3}