+0  
 
+5
144
7
avatar

\(\frac{27x^3-8y^3}{3x-2y}\)

Can this be divided using algebraic long division?

 

(27x- 8y3)/(3x-2y)

 

(if the latex doesn't load)

Guest Feb 27, 2017
edited by Guest  Feb 27, 2017
edited by Guest  Feb 27, 2017

Best Answer 

 #2
avatar
+5

Right, so:

 

27x3 - 8y3 = (3x)3 - (2y)3

 

\(\frac{\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)}{\left(3x-2y\right)}\)

= 9x+ 6xy + 4y2

 

Out of curiosity however, is it possible to use algebraic long division on something like this (with more than 1 variable?)

 

Thanks.

Guest Feb 27, 2017
Sort: 

7+0 Answers

 #1
avatar+89777 
0

(27x3 - 8y3)/(3x-2y)

 

You do not ned to use algebraioc long division.  Use this :))

 

\(\boxed{a^3-b^3=(a-b)(a^2+ab+b^2)}\)

Melody  Feb 27, 2017
 #2
avatar
+5
Best Answer

Right, so:

 

27x3 - 8y3 = (3x)3 - (2y)3

 

\(\frac{\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)}{\left(3x-2y\right)}\)

= 9x+ 6xy + 4y2

 

Out of curiosity however, is it possible to use algebraic long division on something like this (with more than 1 variable?)

 

Thanks.

Guest Feb 27, 2017
 #3
avatar+89777 
0

Hi Guest,

You are lucky that I saw this continued question.  It would be a good idea for you to become a member because then you would be able to send me a private message with a link to this thread and ask me to come back to it again.

PLUS I could be much more sure that you see any late answer that may be added.  :)

 

Yes you can do algebraic division with more than one variable, I have seen other mathematicians use it and I can use it on this one but I am not sure how often it is useful....

 

Doing Algebraic division with LaTex is difficult.

I have done it before with great sucess but it was extremely time consuming. ://

I'll give it a go.

This is different from how I did it before, This is quicker but not quite as nice.

 

\(\begin{array}{llllll}\\ &&9x^2&\color{Maroon}{+4y^2}&\color{NavyBlue}{+6xy}&&\\\hline 3x-2y|&&27x^3&-8y^3\\ &&27x^3&&-18yx^2\\\hline &&&-8y^3&\color{NavyBlue}{+18yx^2}\\ &&&&+18yx^2&-12xy^2\\\hline &&&-8y^3&&\color{Maroon}{+12xy^2}\\ &&&-8y^3&&+12xy^2\\\hline &&&+0&&+0\\\hline \end{array}\)

 

 

Heureka or maybe Max

Could you please show me how to make the horizontal lines the correct length ??  

Melody  Feb 27, 2017
 #4
avatar+18369 
+5

hi Melody,

typesetting polynom division can easy be done with the polynom package:

see: http://tex.stackexchange.com/questions/79182/how-to-draw-polynom-division

 

Example: \((27x^3 - 8y^3)/(3x-2y)\)

\usepackage{polynom}

 

\begin{document}

  

   \textbf{Style A:}\par % this is the default
   \polylongdiv[style=A]{27x^3 - 8y^3}{3x-2y}

  

   \textbf{Style B:}\par
   \polylongdiv[style=B]{27x^3 - 8y^3}{3x-2y}

  

   \textbf{Style C:}\par
   \polylongdiv[style=C]{27x^3 - 8y^3}{3x-2y}

 

\end{document}

 

 

laugh

heureka  Feb 28, 2017
 #5
avatar+89777 
0

 

 

Thanks very much Heureka,

 

But

This does not work in this forum though does it?  I cannot make it work :/ I asume the polynom package is not included. :(

 

Do you do it all directly on your hard drive or do you go to somewhere else on the net to do LaTex like this ?

Melody  Feb 28, 2017
 #6
avatar+18369 
0

Hi Melody,

 

i have installed Latex on my Computer. The setup include a TexStudio.

See picture:

all free-software.

 

Then i have snapped it as image into web2.0calc.

I do it all directly on my hard drive.

 

Here i think we have a minimal latex.

 

laugh

heureka  Feb 28, 2017
 #7
avatar+18369 
0

 

see: https://miktex.org/download

 

...Download and run the Basic MiKTeX installer to setup a basic TeX/LaTeX system on your computer. Please read the tutorial, if you want step-by-step guidance...

 

laugh

heureka  Feb 28, 2017

7 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details