We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:
[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k
In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.
n - m = 2 m - k = 5 k = 10
Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.
