How to simplify the following polynomial of the form P(s)/s?

Question

I want to get an analytic expression for $\frac{P(s)}{s}$ where $P(s)=(s+a)^n-\sum_{i=1}^n b_i a^i(a+s)^{n-i}$ with $a$ a fixed constant and $\sum_{i=1}^n b_i=1$. I want help...

Answer 1

Hint: Use the binomial theorem to write out the powers in terms of a sum in powers of $s$.