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Math Help - Simplify expression

  1. #1
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    Simplify expression

    ({3e}^{2x} - {e}^{-x})({e}^{x} + {3e}^{-2x})

    Need help with the above equation ... Remove brackets and simplify expontential expression !!!

    I got a result of .... after simplifying .... 8e ... i hope its correct ..
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by daemonlies View Post
    ({3e}^{2x} - {e}^{-x})({e}^{x} + {3e}^{-2x})

    Need help with the above equation ... Remove brackets and simplify expontential expression !!!

    I got a result of .... after simplifying .... 8e ... i hope its correct ..
    The answer is
    3^{2x}e^{3x} - 3^{-2x}e^{-3x}

    Show us your work and we can tell you where you went wrong.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark
    The answer is: .  3^{2x}e^{3x} - 3^{-2x}e^{-3x}

    Dan is correct . . . but how far should we simplify?



    Last edited by Soroban; April 28th 2011 at 05:39 AM.
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  4. #4
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    Hi Dan,

    Isn't the middle term of the posted function equal to 1 ?


    bjh
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by bjhopper View Post
    Hi Dan,

    Isn't the middle term of the posted function equal to 1 ?


    bjh
    Sorry. I'm not sure what you mean by "middle term." Here's the solution:
    ((3e)^{2x} - e^{-x})(e^x + (3e)^{-2x})

    = (3e)^{2x}e^x + (3e)^{2x}(3e)^{-2x} - e^{-x}e^x - e^{-x}(3e)^{-2x}

    = 3^{2x}e^{2x}e^x + 1 - 1 - 3^{-2x}e^{-x}e^{-2x}

    = 3^{2x}e^{3x} - 3^{-2x}e^{-3x}

    Please let me know which step you are referring to and we can dissect it.

    -Dan
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  6. #6
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    Hi Dan,
    Thanks for your reply.I did not remove brackets properly and was getting one term in the middle of the other two =1 when I should gotten two terms +1 and -1.



    bjh
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  7. #7
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    This is what i got .....

    (3e^2x - e^(-x) )(e^x+3e^(-2x) )

    3e^3x + 9e - e - 3e^(-3x)

    Cancelled out 3e^3x & - 3e^(-3x)

    9e - e = 8e
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by daemonlies View Post
    This is what i got .....

    (3e^2x - e^(-x) )(e^x+3e^(-2x) )

    3e^3x + 9e - e - 3e^(-3x)

    Cancelled out 3e^3x & - 3e^(-3x)

    9e - e = 8e
    The original problem as written was stated in terms of (3e)^{2x}. In this last post you wrote 3e^{2x}. Which was it supposed to be?

    Otherwise recall the general rule
    (a^n)(a^m) = a^{n + m}

    Let's first talk about the
    e^xe^{-x} = e^{x + -x} = e^0

    by the rule I just mentioned. e^0 = 1, not e.

    Similarly
    (3e)^{2x}(3e)^{-2x} = (3e)^{2x + -2x} = (3e)^0 = 1

    Finally
    3e^{3x} - 3e^{-3x} \neq 0

    I'd recommend you review your exponent rules.

    -Dan

    Edit: If your problem really is
    (3e^{2x} - e^{-x})(e^x + 3e^{-2x})

    then the answer is
    (3e^{2x} - e^{-x})(e^x + 3e^{-2x}) = 3e^{3x} - e^{-3x} + 8

    See if you can get that with what we showed you in this thread.
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  9. #9
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    the edit section is the correct equation ... but wouldnt 3e^3x - e^-3x = 2e .... being the powers cancel out so ... 3e -e = 2e

    Joel
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