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Math Help - expanding brackets

  1. #1
    Member garymarkhov's Avatar
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    expanding brackets

    If you have (AL)^{-1} \left[ (AL)^\frac{1}{2} + BK^\frac{1}{2} \right]^2, is there a way to sneak the (AL)^{-1} into the brackets? Expanding the brackets wouldn't be the end of the world, but it would be nice to know of a better way. It would be especially useful if I ever come across a situation like (AL)^{-1} \left[ (AL)^\frac{1}{2} + BK^\frac{1}{2} \right]^4
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  2. #2
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    Quote Originally Posted by garymarkhov View Post
    If you have (AL)^{-1} \left[ (AL)^\frac{1}{2} + BK^\frac{1}{2} \right]^2, is there a way to sneak the (AL)^{-1} into the brackets? Expanding the brackets wouldn't be the end of the world, but it would be nice to know of a better way. It would be especially useful if I ever come across a situation like (AL)^{-1} \left[ (AL)^\frac{1}{2} + BK^\frac{1}{2} \right]^4
    If you take it inside the brackets, it becomes (AL)^{-1/2}.
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  3. #3
    Member garymarkhov's Avatar
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    Quote Originally Posted by mr fantastic View Post
    If you take it inside the brackets, it becomes (AL)^{-1/2}.
    Super! In the last hour, my basic algebra skills have got a big boost.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    If you take it inside the brackets, it becomes (AL)^{-1/2}.
    Sorry Mr F, but you actually need to exand the square first.

    (AL)^{-1}\left[(AL)^{\frac{1}{2}} + BK^{\frac{1}{2}}\right]^2 = (AL)^{-1}\left[AL + 2(AL)^{\frac{1}{2}}BK^{\frac{1}{2}} + B^2K\right]

     = 1 + 2(AL)^{-\frac{1}{2}}BK^{\frac{1}{2}} + (AL)^{-1}B^2K.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    Sorry Mr F, but you actually need to exand the square first.

    (AL)^{-1}\left[(AL)^{\frac{1}{2}} + BK^{\frac{1}{2}}\right]^2 = (AL)^{-1}\left[AL + 2(AL)^{\frac{1}{2}}BK^{\frac{1}{2}} + B^2K\right]

     = 1 + 2(AL)^{-\frac{1}{2}}BK^{\frac{1}{2}} + (AL)^{-1}B^2K.
    No you don't. eg. a( b + c)^2 =  (a^{1/2} b + a^{1/2} c)^2.

    More generally, a^m (b + c)^n =  (a^{m/n} b + a^{m/n} c)^n.
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    Quote Originally Posted by mr fantastic View Post
    No you don't. eg. a( b + c)^2 = (a^{1/2} b + a^{1/2} c)^2.

    More generally, a^m (b + c)^n = (a^{m/n} b + a^{m/n} c)^n.
    Ah I see... I misread your post. Sorry.

    Still, if you follow the Order of Operations, the Exponentiation should come before the Multiplication anyway...
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