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Math Help - simple algebra question

  1. #1
    Member Jones's Avatar
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    simple algebra question

    Hi

    Shame on me for asking this but

    \bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2

    Do you multiply everything out before subtracting ?
    I got the answer n+1 but it's wrong.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello Jones
    Quote Originally Posted by Jones View Post
    Hi

    Shame on me for asking this but

    \bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2

    Do you multiply everything out before subtracting ?
    I got the answer n+1 but it's wrong.
    No, not if you want the easiest method!

    Note that each term has a common factor \frac{n+1}{2}, so take it out (not forgetting that it has to be squared):

    \bigg(\frac{(n+1)(n+2)}{2}\bigg)^2 - \bigg(\frac{n(n+1)}{2}\bigg)^2= \Big(\frac{n+1}{2}\Big)^2\Big((n+2)^2-n^2\Big)

    Even now, there's no need to multiply out. Use 'difference of two squares' in the second bracket.

    Grandad
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  3. #3
    Member Jones's Avatar
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    Of curse!
    Stupid me.

    Thank you daddy!
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