Finding the term a^8b^9

Question

Find the term that a^8b^9 in the expansion of (2a^2-b)^13

 

Please explain in detail

Answer 1

The coefficient is 2^4 * C(13,4)=11440.

 

The coefficients of a generic expansion of (x+y)^n can be found using:

 

(x+y)^n=∑C(n,i)*x^(n-i)+y^(i), where i iterates from 0 to n.

 

x=2a^2. y=-b. n=13. We're looking for the i=4th term.