[OS X TeX] Binomial Expansion

Claus Gerhardt gerhardt at math.uni-heidelberg.de
Thu Nov 23 13:28:55 EST 2006

```Here is a variant

\newcommand{\Expand}[1]{\polyprint{#1}}

Example

\Expand{(x+1)(x^3+6)^5}

Claus

On Nov 23, 2006, at 19:11, Claus Gerhardt wrote:

> Alain,
>
> Here is my  little birthday present:
>
> \newcommand{\expand}[2]{\polyprint{#1#2}}
>
> Notice that the polynomials have to be delimited by round brackets
> like
>
> \expand{(x+1)}{(x+8)^3}
>
> This will gives you the fully expanded polynomial. A reverse long
> division scheme is a bit more difficult, and frankly, I can't see
> its necessity.
>
> Claus
>
>
> On Nov 23, 2006, at 18:11, Alain Schremmer wrote:
>
>> 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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>
> ------------------------- Info --------------------------
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>

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