ACoPS-proving multinomial theorem

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rakeen
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ACoPS-proving multinomial theorem

Unread post by rakeen » Wed Nov 02, 2011 8:58 am

"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? :(
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nafistiham
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Re: ACoPS-proving multinomial theorem

Unread post by nafistiham » Wed Nov 02, 2011 7:02 pm

\[x+y+z=(x+y)+z\]

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.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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rakeen
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Re: ACoPS-proving multinomial theorem

Unread post by rakeen » Thu Nov 10, 2011 12:10 pm

that's what the problem asked us. To calculate x+(y+z) with binomial theorem to get trinomial and soforth.
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*Mahi*
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Re: ACoPS-proving multinomial theorem

Unread post by *Mahi* » Mon Dec 19, 2011 9:05 pm

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