# [OS X TeX] Binomial Expansion

Alain Schremmer Schremmer.Alain at gmail.com
Thu Nov 23 12:11:07 EST 2006

```Claus Gerhardt wrote:

> Happy Birthday Alain!

Thank you!

> I had a look at the polynom.sty manual. It is only 6 pages and well
> written. You should give it a try.

I did about a year ago and I have been using \polylongdiv ever since.
That was not the point of my post. What I wanted to do over the
Christmas break was to learn a little bit about programming in LaTeX.
The idea was to write, in the spirit of polylongdiv, a command

\Expand{a}{b}{some degree}

that would expand and typeset (a+b)^n. I am still going, The TeX Book in
hand, to try.

> If \Expand{a}{b}{some degree} should represent polynomial division, then
>
> \polylongdiv[stage=3] {(X-1)(X-1)(X^2+1)^4} {(X-1)(X+1)(X+1)}
>
> might be what you want.

Not really since I can expand (a+b)^n in my head and polylongdiv gives
me the output but no source to copy-paste.

Nevertheless, \polylongdiv{(x+a)^{n}}{1}(with an actual value for n) is
indeed very neat and I will try to cut some more from polynom.sty to get
rid of the division (I already got rid of Horner but that was a bit of
trial and error.)

What I wanted was to learn a bit about LaTeX along the theme of writing
the command.

But, indeed, I hadn't realized that polylongdiv could multiply which of
course was dumb since it has to multiply in order to divide (not quite
as in "we had to destroy the city in order to save it" of everlasting fame.)

Of course, what I would kill for is a polylongdiv in ascending order.
But, as I wrote, Heinz didn't respond to my two requests so I think she
or he has better things to do.

Very grateful regards
--schremmer
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