80.6k views
2 votes
Suppose that we wish to expand (x + y + z)17. what is the coefficient of x 2 y5z10

User Jsldnppl
by
7.9k points

1 Answer

2 votes
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.

m - 10 = 5
m = 15

n - 15 = 2
n = 17

Therefore, the coefficient is equal to:

Coefficient = n!/(n-m)!(m-k)!k! = 17!/(17-5)!(15-10)!10! = 408,408


User Ben Scmidth
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories