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Math Help - Rewriting an equation.

  1. #1
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    Rewriting an equation.

    Could somebody explain how we get the 2nd equation from the 1st?
    1) 3 (x − 3)^3 (x + 5)^2 − 3 (x + 5)^3 (x − 3)^2

    2) 3 (x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]
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  2. #2
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    Quote Originally Posted by p75213 View Post
    1) 3(x − 3)^3 (x + 5)^2 − 3(x + 5)^3 (x − 3)^2

    2) 3(x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]
    let a = x-3 and b = x+5
    3a^3 b^2 - 3a^2 b^3
    3a^2 b^2(a - b)
    Kapish?
    Last edited by Wilmer; March 31st 2010 at 06:57 PM. Reason: correct typo
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  3. #3
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    Sorry. Still don't get it. Wouldn't 3a^2b^2(a-b) expand into 3a^3b^2-3a^2b^3. Seems like I am missing something here.
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  4. #4
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    Quote Originally Posted by p75213 View Post
    Could somebody explain how we get the 2nd equation from the 1st?
    1) 3 (x − 3)^3 (x + 5)^2 − 3 (x + 5)^3 (x − 3)^2

    2) 3 (x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]

    I think they just factored out a common term:


    If you were to multiply it out, you should get back to the first expression.
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  5. #5
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    Quote Originally Posted by p75213 View Post
    Wouldn't 3a^2b^2(a-b) expand into 3a^3b^2-3a^2b^3.
    Yes. I made typo; now corrected. But still same idea...
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  6. #6
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    Yep - that's it. Many thanks.
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