Question

Which of the following is the third term of the expansion (a + b)^n ?

C(n, 2)a^n - 2b^2
C(n, 3)a^n - 3b
C(n, 2)a^2b^n - 2

Answer 1

C(n, 2)a^(n-2)b^2

Explanation:

Generally, the expansion is written in decreasing powers of "a", so the first few terms would have variable constellations that look like ...

a^n, a^(n-1)b, a^(n-2)b^2, ...

The coefficients would be (in order), C(n, k) for k increasing from 0, so the coefficient of the 3rd term would be C(n, 2).