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Math Help - Simplify (6a^2 + a - 2)(2a^2 - 3a + 1)

  1. #1
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    Simplify (6a^2 + a - 2)(2a^2 - 3a + 1)

    hey im having trouble with this. pleas help me figure out how to do this problem. i have a test tomorrow and really need this help...im sorry im a noob. Simplify (6a^2 + a - 2)(2a^2 - 3a + 1)-math-proble-m.jpg
    Last edited by mr fantastic; November 19th 2010 at 09:14 PM. Reason: Re-titled.
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  2. #2
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    Factor the top and bottom: \displaystyle (3a\pm     x )(2a\pm     y ) = 6a^2 + a - 2 \ \ni x,y\in\mathbb{Z} and do the same for the denominator
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  3. #3
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    Quote Originally Posted by greenzspy View Post
    hey im having trouble with this. pleas help me figure out how to do this problem. i have a test tomorrow and really need this help...im sorry im a noob. Click image for larger version. 

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    you need to factor the numerator and denominator and divide out the common factor ...

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  4. #4
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    Recognise that

    6a^2+a-2 = (3a+2)(2a-1) and
    2a^2-3a+1 = (2a-1)(a-1).

    Putting these together, we obtain

     \frac{6a^2 + a - 2}{(2a^2 - 3a + 1} = \frac{(3a+2)(2a-1)}{(2a-1)(a-1)}=\frac{3a+2}{a-1},

    where the last step is done under the assumption that

    a\ne\frac{1}{2}_{.}

    If we do not have this assumption, we cannot do the cancellation.
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