Question

Expand: (x+y^2+z)^6

Answer 1

This is a trinomial expansion, not binomal

We can make it fit the binomial expansion by doing something like
let a = x + y^2, then your question becomes
(a + z)^6 , and know we need coefficients of 1, 6, 15, 20, 15, 6, 1
= a^6 + 6a^5 z + 15a^4 z^2 + 20a^3 z^3 + 15a^2 z^4 + 6a z^5 + z^6

now replace each z value by x+y^2 and expand each of those powers
e.g. from 15a^4 z^2, we would get
15(x+y^2)^4 z^2
where (x+y^2)^4 = x^4 + 4x^3 y^2 + 6x^2 y^4 + 4x y^6 + y^8
and 15a^4 z^2 would become
15(x^4 + 4x^3 y^2 + 6x^2 y^4 + 4x y^6 + y^8)(z^2)
Now expand this!!!! and that is just one term, and of course when
you are done with each of the expansions, there will be lots of like terms.

the probability of making an error is quite high, and no professor
in his/her right mind would actually expect you to complete this.
btw, here is Wolfram's answer:

www.wolframalpha.com/input/?i=expand+%28x%2By%5E2%2Bz%29%5E6

Answer 2

google trinomial coefficients for handy (but still) complicated formulas and arrays