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# Algebraic long division

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## $$\frac{27x^3-8y^3}{3x-2y}$$

Can this be divided using algebraic long division?

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

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

#2
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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
#1
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(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

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
+94118
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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
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hi Melody,

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

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
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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
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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
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