Algebraic long division

Right, so:

27x³ - 8y³ = (3x)³ - (2y)³

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

= 9x² + 6xy + 4y²

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

Thanks.

(27x3 - 8y3)/(3x-2y)

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

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

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 ??