## ACoPS-proving multinomial theorem

For students of class 11-12 (age 16+)
rakeen
Posts: 384
Joined: Thu Dec 09, 2010 5:21 pm
Location: Dhaka

### ACoPS-proving multinomial theorem

"Expand (x + y + z)2 and
(x + y + z)3 with multinomial theorem(using binomial). Think about what make the coefficients
what they are."

if we expand $(x+y+z)^2$ algeraically then we'll see that there's no binomial coefficient(yeah I know there shouldn't be.it should be trinomial coefficient.and I'm trying to find that)! Like $x^2+ y^2 + z^2 + 2xy + 2yz + 2zx$ - 1,2,1,2,1 and 2.That means we need to try something(add something and use symmetry may be!) to get those coefficients. How can I do that?
r@k€€/|/

nafistiham
Posts: 829
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Location: 24.758613,90.400161
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### Re: ACoPS-proving multinomial theorem

$x+y+z=(x+y)+z$

so, every multinomial can be turned into a binomial.

of course, it is very hard to calculate.but, if you want such kind of theorem, (i don't know if there is any or not) those calculations would also be difficult.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

rakeen
Posts: 384
Joined: Thu Dec 09, 2010 5:21 pm
Location: Dhaka

### Re: ACoPS-proving multinomial theorem

that's what the problem asked us. To calculate x+(y+z) with binomial theorem to get trinomial and soforth.
r@k€€/|/

*Mahi*
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### Re: ACoPS-proving multinomial theorem

Use $L^AT_EX$, It makes our work a lot easier!