Hello,

In the expansion of (x1 + x2 + x3)^10, what is the coefficient of the x^22?

How we can solve this kind of problems can you explain me?

Thank you.

Printable View

- Dec 14th 2013, 10:57 PMsunriseA binom question
Hello,

In the expansion of (x1 + x2 + x3)^10, what is the coefficient of the x^22?

How we can solve this kind of problems can you explain me?

Thank you. - Dec 14th 2013, 11:03 PMromsekRe: A binom question
just to be clear do you mean

what you want is the multinomial theorem Multinomial theorem - Wikipedia, the free encyclopedia

and you'd let , , - Dec 14th 2013, 11:21 PMsunriseRe: A binom question
Yes romsek,

I mean(x^1+x^2+x^3)^10

I prefer, waiting of friends explanations. Thank you. - Jan 3rd 2014, 11:16 AMHallsofIvyRe: A binom question
I think I would be inclined to do it this way:

So that, for every n, we will have provided the power of x in is 30- 3n- 22= 8- 3n. Of course, so x will have power 8- 3n when 2i+ n- i= i+ n= 8- 3n or i= 8- 4n. The coefficient of that power will be .

Since that is for every n, the coefficient of will be - Jan 4th 2014, 01:15 AMsunriseRe: A binom question
Thank you very much