Question

What is the third term in the expansion of`(cos x+3)^5`?

Answer 1

We use the formula `t_(k + 1)=color(white)(two)_nC_k(x)^(n - k) xx y^k`, where `color(white)(two)_nC_k` denotes the combination formula in the context of `(x + y)^n`.

Since we're looking for the third term, `k + 1 = 3 ->k = 2`.

`t_3 = color(white)(two)_5C_2 xx (cosx)^(5 - 2) xx 3^2`

`t_3 = (5!)/((5 - 2)! xx 2!) xx (cosx)^3 xx 9`

`t_3 = 10 xx cos^3x xx 9`

`t_3 = 90cos^3x`

Hopefully this helps!