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Math Help - Factoring Differences of Cubes

  1. #1
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    Factoring Differences of Cubes

    I'm having trouble factoring this particular difference of cubes. Could someone please show me step by step how to approach this?

    The expression is:

    (1/512x)^9 -512



    Thanks!!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by MATHDUDE2 View Post
    I'm having trouble factoring this particular difference of cubes. Could someone please show me step by step how to approach this?

    The expression is:

    (1/512x)^9 -512



    Thanks!!
    We need to use the exponential law that (x^a)^b=x^{ab}

    \left[\left( \frac{1}{512x} \right)^3\right]^3-(2^3)^3=...

    So we can identify a=\left( \frac{1}{512x} \right)^3 and b=2^3=8
    a^3-b^3=(a-b)(a^2-ab+b^2) so just plug into the formula from here
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  3. #3
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    thanks!
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