Factoring sum of cubes

Factoring sum 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 sum of cubes

    i. What is sum of cubes?

    ii. How can sum of cubes be factored?


  • 2.
    Factoring Using the Sum of Cubes Formula

    Factor the following expressions:

    a)
    x3+125x^{3} + 125

    b)
    x3+827x^{3} + \frac{8}{27}


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

    Factor the following expressions:

    a)
    64x3+164x^{3} + 1

    b)
    125x6+8125x^{6} + 8


  • 4.
    Factoring Binomials with 2 variables

    Factor the following expressions:

    a)
    8x6+27y98x^{6} + 27y^{9}

    b)
    x12y6+64x^{12}y^{6} + 64


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

    Factor the following expressions:

    a)
    x38-x^{3} - 8

    b)
    54x3+12854x^{3} + 128

    c)
    81x10y+24xy781x^{10}y + 24xy^{7}


  • 6.
    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?