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Math Help - Factor the polynomial

  1. #1
    LaSha
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    Question Factor the polynomial

    Could you show me how to factor the polynomial to these problems?
    1. w^2b^2-1
    2. 27a^b-12b^3
    3. s^2m^2-1
    4. 108a^4b-75b^3
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  2. #2
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by LaSha View Post
    Could you show me how to factor the polynomial to these problems?
    1. w^2b^2-1
    2. 27a^b-12b^3
    3. s^2m^2-1
    4. 108a^4b-75b^3
    1. This can be factored using a method called DOPS (Difference of Perfect Squares), i.e. a^2 - b^2 = (a-b)(a+b).

    w^2b^2-1 = (wb+1)(wb-1) = (bw+1)(bw-1)

    (As a general rule of thumb, try to place your variables in alphabetical order)

    3. Same thing:

    s^2m^2-1 = (sm+1)(sm-1)


    The other two look very ugly to factor, are you sure you typed #2 correctly?
    Last edited by DivideBy0; April 23rd 2007 at 02:54 AM.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by LaSha View Post
    4. 108a^4b-75b^3
    There is a common 3b between the terms:\
    108a^4b-75b^3 = 3b(36a^4 - 25b^2)

    Now note that the second factor here is the difference between two squares:
    = 3b(6a^2 + 5b)(6a^2 - 5b)

    -Dan
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