Can this be divided using algebraic long division?

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

(if the latex doesn't load)

Guest Feb 27, 2017

edited by
Guest
Feb 27, 2017

edited by Guest Feb 27, 2017

edited by Guest Feb 27, 2017

#2**+5 **

Right, so:

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

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

= 9x^{2 }+ 6xy + 4y^{2}

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

#1**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**+5 **

Best Answer

Right, so:

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

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

= 9x^{2 }+ 6xy + 4y^{2}

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**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**+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}

heureka
Feb 28, 2017

#5**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**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.

heureka
Feb 28, 2017

#7**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...

heureka
Feb 28, 2017