Factoring sum of cubes

  1. Introduction to factoring sum of cubes

    i. What is sum of cubes?

    ii. How can sum of cubes be factored?

  1. Factoring Using the Sum of Cubes Formula

    Factor the following expressions:

    1. x3+125x^{3} + 125
    2. x3+827x^{3} + \frac{8}{27}
  2. Factoring Using the Sum of Cubes Formula - Extended

    Factor the following expressions:

    1. 64x3+164x^{3} + 1
    2. 125x6+8125x^{6} + 8
  3. Factoring Binomials with 2 variables

    Factor the following expressions:

    1. 8x6+27y98x^{6} + 27y^{9}
    2. x12y6+64x^{12}y^{6} + 64
  4. First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula

    Factor the following expressions:

    1. x38-x^{3} - 8
    2. 54x3+12854x^{3} + 128
    3. 81x10y+24xy781x^{10}y + 24xy^{7}
  5. 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?

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    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)?