Question

Find the 3rd term in the expansion of (a + b)^7 in simplest form.

Answer 1

9514 1404 393Answer:

21·a^5·b^2

Explanation:

The k-th term is ...

C(7, k)·a^(7-k)·b^k . . . . . where k counts from 0 to n

Then k=2 for the third term. The coefficient of it is ...

C(7, 2) = 7!/(2!(7-2)!) = 7·6/(2·1) = 21

The third term is ...

21·a^5·b^2