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Thread: need help with basic algebra problem

  1. #1
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    need help with basic algebra problem

    the problem is:

    (x^2 - y^2)^2 / x^2 + 2xy + y2

    the answer is supposed to be:

    x^2 - 2xy +y2

    i get to x^2 - 2x^2y^2 + y^2 / 2xy

    what am i missing?

    thanks
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by cornman View Post
    the problem is:

    (x^2 - y^2)^2 / x^2 + 2xy + y2

    the answer is supposed to be:

    x^2 - 2xy +y2

    i get to x^2 - 2x^2y^2 + y^2 / 2xy

    what am i missing?

    thanks
    You need to split your numerator into $\displaystyle (x^2-y^2)(x^2-y^2)$ and FOIL it to get $\displaystyle x^4 - 2x^2y^2 + y^4$ then cancel.
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by cornman View Post
    the problem is:

    (x^2 - y^2)^2 / x^2 + 2xy + y2

    the answer is supposed to be:

    x^2 - 2xy +y2

    i get to x^2 - 2x^2y^2 + y^2 / 2xy

    what am i missing?

    thanks

    $\displaystyle
    {(x^2-y^2) =(x+y)(x-y)}

    $

    $\displaystyle
    {(x+y)^2 = (x^2 +2xy +y^2) }
    $

    $\displaystyle
    {(x-y)^2 = (x^2-2xy +y^2)}
    $

    $\displaystyle
    (x^2-y^2)^2 =(x+y)^2(x-y)^2...........\text{Use in numerator}

    $

    $\displaystyle
    (x^2 +2xy +y^2)= (x+y)^2 ...........\text{Use in denominator}
    $


    $\displaystyle
    (x^2-2xy +y^2)=(x-y)^2 ...........\text{use in the last step}

    $
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