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Math Help - Expanding a tricky integrand involving exponents

  1. #1
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    Expanding a tricky function involving exponents

    Why does the expansion of -

    [(e^x)/12 - 3(e^-x)]^2

    contain a (-1/2)?

    Note: when expanded --> [(e^2x)/144 - 9(e^-2x) -1/2]

    Shouldn't it just be the first two terms?

    Thanks in advance!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Re: Expanding a tricky function involving exponents

    Quote Originally Posted by bhaktir View Post
    Why does the expansion of -

    [(e^x)/12 - 3(e^-x)]^2

    contain a (-1/2)?

    Note: when expanded --> [(e^2x)/144 - 9(e^-2x) -1/2]

    Shouldn't it just be the first two terms?

    Thanks in advance!
    Recall that (a-b)^2=a^2-2ab+b^2. So in this case -2ab =-2\left(\tfrac{1}{12}e^x\right)\left(3e^{-x}\right) = -2\left(\tfrac{1}{4}\right)=-\tfrac{1}{2}.

    Does this make sense?
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  3. #3
    Member anonimnystefy's Avatar
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    Re: Expanding a tricky function involving exponents

    hi

    the formula for the square of a difference is:

    (a-b)^2=a^2-2ab+b^2

    If a=\frac{e^x}{12} and b=\frac{3}{e^x}

    then:

    (a+b)^2=a^2+2ab+b^2=(\frac{e^x}{12})^2-2\cdot\frac{e^x}{12}\cdot\frac{3}{e^x}+(\frac{3}{e  ^x}

    try it now.
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  4. #4
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    Re: Expanding a tricky function involving exponents

    OH! (a-b)^2

    I can't believe I forgot that! Calc III is messing with my head. :/

    Thanks again for the swift responses!! This site has been extremely helpful!
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