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Math Help - Expand and simplify help?

  1. #1
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    Expand and simplify help?

    (2a-3b)cubed (i dunno how to make a little 3)

    I have nooo clue how to even start with this O_O
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kais View Post
    (2a-3b)cubed (i dunno how to make a little 3)

    I have nooo clue how to even start with this O_O
    You should know several ways to do this, one is to multiply out:

    ((2a-3b)(2a-3b))(2a-3b)=(4a^2-12ab+9b^2)(2a-3b)=\ ...

    another is to expand using Pascalls triangle/binomial theorem:

    (2a-3b)^3=(2a)^3+3(2a)^2(-3b)+3(2a)(-3b)^2+(-3b)^3=\ ...

    CB
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  3. #3
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    Quote Originally Posted by kais View Post
    (2a-3b)cubed (i dunno how to make a little 3)

    I have nooo clue how to even start with this O_O
    use identity

     (x-y)^3= x^3-y^3-3x^2y+3ab^2
    in this case put x= 2a and y= 3b
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  4. #4
    MHF Contributor Amer's Avatar
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    (a-b)^3=a^3-3ab^2-3ba^2-b^3
    Last edited by Amer; October 30th 2009 at 08:41 AM.
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  5. #5
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    Hmm,

    I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by kais View Post
    Hmm,

    I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?
    The final result will contain terms of order 3, so there will be terms containing the cube of a and of b, as well as terms containing a^2b and ab^2

    CB
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  7. #7
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    Quote Originally Posted by kais View Post
    I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?
    Post a squared this way : a^2 ; a cubed : a^3

    4a^2 - 12ab + 9b^2 is what you get from (2a - b) times (2a - b);
    now you need to multiply (4a^2 - 12ab + 9b^2) times (2a - b);
    then you're finished.
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