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Math Help - Simplify?

  1. #1
    a.a
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    Question Simplify?

    Is it possible to simplify (2pi^3)/3 - (2pir^3)/(3sqrt.3)
    the furthest I was able to go was (2sqrt.3 r^3 - 2pi r^3) / (3sqrt.3)
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  2. #2
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    \frac{2\pi^{3} }{3}  \cdot {\color{blue} \frac{\sqrt{3}}{\sqrt{3}}} \:\: - \:\: \frac{2\pi r^{3}}{3 \sqrt{3}} = \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}}

    Not much else you can do ... unless you factor a bit but that doesn't do a whole lot:
    \frac{2\pi \left(\pi^{2} \sqrt{3} - r^{3}\right)}{3\sqrt{3}}
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  3. #3
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    What if you were to rationalize the denominator?
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  4. #4
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    Sure:
    \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}} \cdot {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}

    = \frac{6\pi^{3} - 2\pi r^{3} \sqrt{3}}{{\color{red}9}}

    Doesn't change it too much. I don't think it matters too much at this point how the expression is represented.

    Edited.
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  5. #5
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    Quote Originally Posted by o_O View Post
    Sure:
    \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}} \cdot {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}

    = \frac{6\pi^{3} - 2\pi r^{3} \sqrt{3}}{3}

    Doesn't change it too much. I don't think it matters too much at this point how the expression is represented.
    Wouldn't it be 9 in the denominator?
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  6. #6
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    Yes, just a typo. Nonetheless, it really doesn't matter what it is represented as at this point.
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