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Math Help - [Factorization] Factorization of Square factors

  1. #1
    Junior Member Cthul's Avatar
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    [Factorization] Factorization of Square factors

    How do I factorize (further) this? I do not understand the steps, I know the answer although.

    The question goes:

    1)
    (x-b)^2-x+b

    =(x-b)^2-(x-b)
    =(x-b)(x-b-1)

    I do not understand the steps from 2nd to 3rd.

    2)
    x^2-y^2-(x-y)^2

    =(x-y)(x+y)-(x-y)^2
    =(x-y)[x+y-(x-y)]
    =(x-y)(x+y-x+y)
    =(x-y)(2y)
    =2y(x-y)

    I do not get the step from 1 to 2.

    Explanation would be appreciated.
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  2. #2
    Member u2_wa's Avatar
    Joined
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    Quote Originally Posted by Cthul View Post
    How do I factorize (further) this? I do not understand the steps, I know the answer although.

    The question goes:

    1)
    (x-b)^2-x+b

    =(x-b)^2-(x-b)
    =(x-b)(x-b-1)

    I do not understand the steps from 2nd to 3rd.



    Explanation would be appreciated.
    Suppose the equation is as such: a^2-a
    To simplify it take a common i.e a(a-1)

    In the same way take (x-b) common from (x-b)^2-(x-b) i.e
    (x-b)[(x-b)-1].

    You could also do it by substituting a with (x-b) in equation a(a-1)=(x-b)[(x-b)-1]

    Hope this helps!!!
    Last edited by u2_wa; March 4th 2010 at 02:51 AM.
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  3. #3
    Member u2_wa's Avatar
    Joined
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    Quote Originally Posted by Cthul View Post
    How do I factorize (further) this? I do not understand the steps, I know the answer although.


    2)
    x^2-y^2-(x-y)^2

    =(x-y)(x+y)-(x-y)^2
    =(x-y)[x+y-(x-y)]
    =(x-y)(x+y-x+y)
    =(x-y)(2y)
    =2y(x-y)

    I do not get the step from 1 to 2.

    Explanation would be appreciated.

    Do you know this identity (a+b)(a-b)=a^2-b^2

    To solve this equation : \color{red}x^2-y^2\color{black}-(x-y)^2

    \color{red}(x+y)(x-y)\color{black}-(x-y)^2

    Hope this helps!!
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