Results 1 to 3 of 3

Math Help - Problem with cancelling indicies

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    72

    Problem with cancelling indicies

    Hi,

    im working through a worked example from a text, I have got to the point where I am cancelling the indicies. The text has missed out the cancelling process and I cant see how they have done it, any tips would be appreciated.

    {7^2n-7^n-1.(-5)^n+1-(-5)^n-1.7^n+1 +(-5)^2n} - {7^2n -2(7^n(-5)^n)+(-5)^2n}

    After cancelling this we get( this is the bit im having trouble with)

    7^n-1(-5)^n-1 x {-(-5)^2 - 7^2 + 2 x 7 x (-5)}

    Any hints would be greatly apreciated

    p.s not sure if i have posted this in the right part of the forum

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    772
    Hello, offahengaway and chips!

    We could have used more parentheses around the exponents, too.


    7^{2n}-7^{n-1}(\text{-}5)^{n+1}-(\text{-}5)^{n-1}7^{n+1} +(\text{-}5)^{2n} - \bigg[7^{2n} -2\cdot7^n(\text{-}5)^n+(\text{-}5)^{2n}\bigg]

    After cancelling: . 7^{n-1}(\text{-}5)^{n-1}\cdot\bigg[-(\text{-}5)^2 - 7^2 + 2\!\cdot\!7\!\cdot(\text{-}5)\bigg]

    We have: . {\color{blue}\rlap{///}}7^{2n} - 7^{n-1}(\text{-}5)^{n+1} - 7^{n+1}(\text{-}5)^{n-1} + {\color{red}\rlap{////}}(\text{-}5)^{2n} - {\color{blue}\rlap{///}}7^{2n} + 2\!\cdot\!7^n(\text{-}5)^n - {\color{red}\rlap{////}}(\text{-}5)^{2n}

    . . . . . = \;-7^{n-1}(\text{-}5)^{n+1} - 7^{n+1}(\text{-}5)^{n-1} + 2\!\cdot\!7^n(\text{-}5)^n


    Factor out: . 7^{n-1}(\text{-}5)^{n-1}\bigg[-(\text{-}5)^2 - 7^2 + 2\!\cdot\!7\!\cdot\!(\text{-}5)\bigg]

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    More information please

    Hello offahengaway and chips
    Quote Originally Posted by offahengaway and chips View Post
    Hi,

    im working through a worked example from a text, I have got to the point where I am cancelling the indicies. The text has missed out the cancelling process and I cant see how they have done it, any tips would be appreciated.

    {7^2n-7^n-1.(-5)^n+1-(-5)^n-1.7^n+1 +(-5)^2n} - {7^2n -2(7^n(-5)^n)+(-5)^2n}

    After cancelling this we get( this is the bit im having trouble with)

    7^n-1(-5)^n-1 x {-(-5)^2 - 7^2 + 2 x 7 x (-5)}

    Any hints would be greatly apreciated

    p.s not sure if i have posted this in the right part of the forum

    thanks
    It's very difficult to read it in the format you have given us. Why not learn how to do it using LaTeX? Just click on any line of my coding, and the LaTeX code will pop up in a new little window.

    What you have, I think, is:

    \Big(\color{blue}7^{2n}\color{black}-7^{n-1}.(-5)^{n+1}-(-5)^{n-1}.7^{n+1} +\color{blue}(-5)^{2n}\color{black}\Big) -\Big(\color{blue}7^{2n}\color{black} -2.7^n.(-5)^n+\color{blue}(-5)^{2n}\color{black}\Big)

    The terms that I have marked in
    blue are then eliminated when we subtract, and we are left with:

    -7^{n-1}.(-5)^{n+1}-(-5)^{n-1}.7^{n+1} +2.7^n.(-5)^n

    Now look for the highest common factor of all three of these terms. This is \color{red}7^{n-1}.(-5)^{n-1}. So we can write this expression as:

    -\color{red}7^{n-1}.(-5)^{n-1}\color{black}.(-5)^2-\color{red}7^{n-1}.(-5)^{n-1}\color{black}.7^2 +\color{red}7^{n-1}.(-5)^{n-1}\color{black}.2.7.(-5)

    So when we take out this common factor, we get:

    \color{red}7^{n-1}.(-5)^{n-1}\color{black}\Big(-(-5)^2-7^2+2.7.(-5)\Big)

    OK now?

    Grandad

    PS I see Soroban got there first. Ah well, great minds ...
    Last edited by Grandad; March 25th 2009 at 08:34 AM. Reason: Add PS
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maple cancelling fractions problem
    Posted in the Math Software Forum
    Replies: 0
    Last Post: May 2nd 2010, 10:34 AM
  2. Cancelling Rules
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 30th 2010, 11:45 AM
  3. Indicies Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 2nd 2009, 03:52 AM
  4. cancelling in fractions
    Posted in the Algebra Forum
    Replies: 6
    Last Post: June 10th 2008, 01:08 AM
  5. Cancelling down
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 13th 2008, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum