Help me please!

Question

If you expand the binomial expression (x + y)^9, there will be 10 terms. What is the coefficient of the third term?

Answer 1

(x+y)⁹=x⁹+9x⁸y+36x⁷y²+84x⁶y³...

coefficient of the third term is 36

Answer 2

Hello, thank you for taking the time to post your question!

For the third term we have n = 9 and the term number is 3, meaning that k = 3 – 1 = 2

What that means is that we’re doing 9C2 (9 choose 2) to find what the coefficient term would be for this binomial expression

For that value I get

9! / (2!(9-2)!) = 9! / 2!7! = 9 x 8 / 2 x 1 = 72/2 = 36

So the coefficient of the third term here is 36

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)