"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?

## ACoPS-proving multinomial theorem

### ACoPS-proving multinomial theorem

r@k€€/|/

- nafistiham
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
**Contact:**

### 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.

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.

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

### 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€€/|/

### Re: ACoPS-proving multinomial theorem

Please read Forum Guide and Rules before you post.

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

Nur Muhammad Shafiullah | Mahi

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

Nur Muhammad Shafiullah | Mahi