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Math Help - Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

  1. #1
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    Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b-algebra.png
    I'm having a hard time understanding how to go about simplifying this expression.
    Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

    I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

    If anyone can offer some advice that would be much appreciated.
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  2. #2
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    (x^a)^b = x^{a\cdot b}
    \dfrac{1}{x^a} = x^{-a}

    So, yes, you should FOIL the exponents.
    Thanks from justincase13
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  3. #3
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    Quote Originally Posted by justincase13 View Post
    Click image for larger version. 

Name:	algebra.png 
Views:	2 
Size:	4.1 KB 
ID:	30982
    I'm having a hard time understanding how to go about simplifying this expression.
    Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

    I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

    If anyone can offer some advice that would be much appreciated.
    well let's take a look

    $\Large \dfrac{\left(x^{a+b}\right)^{a-b}}{\left(x^{a-2b}\right)^{a+2b}}=$

    $\Large \dfrac {x^{(a+b)(a-b)}}{x^{(a-2b)(a+2b)}}=$

    $\Large \dfrac{x^{a^2-b^2}}{x^{a^2-4b^2}}=$

    $\Large \dfrac{x^{a^2}x^{-b^2}}{x^{a^2}x^{-4b^2}}=$

    $\Large x^{3b^2}$

    $\Large -b^2 - (-4b^2)=3b^2$
    Thanks from justincase13
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  4. #4
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    Thanks so much guys...can I also think of it like this ? Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b-math.jpg
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  5. #5
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    You cannot cancel the x's. The answer is

    x^{a^2-b^2}x^{-(a^2-4b^2)} = x^{a^2-b^2-(a^2-4b^2)} = x^{a^2-a^2+4b^2-b^2} = x^{3b^2}

    So, the a^2 cancels, but the x does not.
    Thanks from justincase13 and topsquark
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  6. #6
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    Quote Originally Posted by justincase13 View Post
    Thanks so much guys...can I also think of it like this ? Click image for larger version. 

Name:	MATH.jpg 
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ID:	30988
    don't cross out your x's, but yeah, I suppose you could look at it like that as long as you understand what it means.
    Thanks from justincase13
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  7. #7
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    Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

    Quote Originally Posted by justincase13 View Post
    Click image for larger version. 

Name:	algebra.png 
Views:	2 
Size:	4.1 KB 
ID:	30982
    I'm having a hard time understanding how to go about simplifying this expression.
    Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

    I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

    If anyone can offer some advice that would be much appreciated.
    just multiply the exponents respectively

    x^ [(a^2-b^2) -(a^2-4b^2)] = x^ 3b^2
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