Factoring sum of cubes

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Introduction
Lessons
  1. Introduction to factoring sum of cubes

    i. What is sum of cubes?

    ii. How can sum of cubes be factored?

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Examples
Lessons
  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)?