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Math Help - can't recall algebra

  1. #1
    Newbie
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    Smile can't recall algebra

    Here is the problem:
    step 1: k(k-1)^2 - k(k-1)
    step 2: (k-1) [ k(k-1) - k]

    now, the answer says the next line is this,

    step 3: (k-1) [(k-1)^2 -1]

    I'm confused how it goes from step 2 to step 3. There is something I've forgotten and cannot figure out how to go from step 2 to step 3. thanks.
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  2. #2
    Senior Member I-Think's Avatar
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    (k-1) [ k(k-1) - k]

    (k-1)[k^2-k-k]

    (k-1)[k^2-2k]  N.B.: (k-1)^2=k^2-2k+1\rightarrow{(k-1)^2-1=k^2-2k}

    (k-1)[(k-1)^2-1]
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  3. #3
    MHF Contributor
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    Quote Originally Posted by tigertina View Post
    Here is the problem:
    step 1: k(k-1)^2 - k(k-1)
    step 2: (k-1) [ k(k-1) - k]
    now, the answer says the next line is this,
    step 3: (k-1) [(k-1)^2 -1]
    I'm confused how it goes from step 2 to step 3.
    From k(k-1) - k to (k-1)^2 - 1 :

    k(k-1) - k = k^2 - k - k = k^2 - 2k

    (k-1)^2 - 1 = k^2 - 2k + 1 - 1 = k^2 - 2k

    OK?
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