# Thread: Problem with cancelling indicies

1. ## 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

2. Hello, offahengaway and chips!

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

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

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

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

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

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

Hello offahengaway and chips
Originally Posted by offahengaway and chips
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:

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

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

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

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

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

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

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

OK now?