201k views
0 votes
What is the coefficient of x^5y^5 in the expansion of (x+y)^10

User Sandoz
by
7.9k points

1 Answer

1 vote

Answer:

252

Explanation:

We know the binomial expansion of


(a + x)^(n) = a^(n) + C_(1)a^((n - 1)) x + C_(2) a^((n - 2)) x^(2) + ........ + C_(r) a^((n - r)) x^(r) + ........ + x^(n)

Therefore, in the binomial expansion of
(x + y)^(10) the term with
x^(5)y^(5) expression will be there when r = 5

Hence, the term will be
^(10)C_(5) x^(5) y^(5).

Therefore, the coefficient of
x^(5)y^(5) will be


^(10)C_(5) = (10!)/(5! * 5!) = 252 (Answer)

User Chad Skeeters
by
7.9k 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