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?
what you want is the multinomial theorem Multinomial theorem - Wikipedia, the free encyclopedia
and you'd let , ,
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