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Math Help - Simplifying: difference of two cubes

  1. #1
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    Simplifying: difference of two cubes

    <br />
\frac {x^2 - 27}{x - 3} <br />
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Tenskypoo View Post
    <br />
\frac {x^2 - 27}{x - 3} <br />
    based on your previous questions, it makes me feel this should be \frac {x^3 - 27}{x - 3} ...is that right?
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    yup. I've gotten to where it is


    (x+27)(x^2 - (x times 27))+ 27^2
    __________________________________
    x-3

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    Quote Originally Posted by Tenskypoo View Post
    yup. I've gotten to where it is


    (x+27)(x^2 - (x times 27))+ 27^2
    __________________________________
    x-3

    nope

    ok, so if it is x^3 - 27 on top. you would write that as x^3 - 3^3 and apply the (difference of two cubes) formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
    Last edited by Jhevon; April 7th 2009 at 10:35 PM.
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  5. #5
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    ah, because 3 x 3 x 3= 27

    So if it was, x^4 - 16 it would be x^4 - 2^4 just as an example to see if i understand.
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    Quote Originally Posted by Tenskypoo View Post
    ah, because 3 x 3 x 3= 27

    So if it was, x^4 - 16 it would be x^4 - 2^4 just as an example to see if i understand.
    ah, yeah, you could write it like that. but the formula i gave does not apply to that expression. but yes, that's the idea
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    Quote Originally Posted by Jhevon View Post
    nope

    ok, so if it is x^3 - 27 on top. you would write that as x^3 - 3^3 and apply the (difference of two cubes) formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
    so would it be

    x^3 - 3^3 = (x - 3)(x^2 + (x times 3) + 3^2)
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    Quote Originally Posted by Tenskypoo View Post
    so would it be

    x^3 - 3^3 = (x - 3)(x^2 + (x times 3) + 3^2)
    yes, that's the numerator
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  9. #9
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    i'd put that over x-3, but cancel out the x-3 since it is in both the numer. and denom. therefore leaving me with

     x^2 + 3x + 9

    i may have done the part wrong, or it isn't simplified enough
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  10. #10
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    Quote Originally Posted by Tenskypoo View Post
    i'd put that over x-3, but cancel out the x-3 since it is in both the numer. and denom. therefore leaving me with

     x^2 + 3x + 9

    i may have done the part wrong, or it isn't simplified enough
    that is fine
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  11. #11
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    Quote Originally Posted by Tenskypoo View Post
    yup. I've gotten to where it is


    (x+27)(x^2 - (x times 27))+ 27^2
    __________________________________
    x-3

    Make sure you learn and memorize the formula for factoring a difference of cubes before the next test!
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