How to Deduce the Coefficient of x^n in the Expansion of (x+3)(1+2x)^(-2)?

[elitewarr]

Homework Statement

By finding the first 4 terms in the expansion of (1+2x)^(-2) in ascending powers of x and find the coefficient of x^n term. Hence deduce the coefficient of x^n term in the expansion of (x+3)(1+2x)^(-2).

Homework Equations

The Attempt at a Solution

The first two parts were easy. For the first part, the answer is 1 - 4x + 12x^2 - 32x^3 + ...
For the second part, [(-1)^n](n+1)(2^n). But I'm stunned at the last part. How do I deduce?

 

[rock.freak667]

Well the only term that will give you an 'x' term is if you multiply an x by an x. So if you multiply the xⁿ term by the x, you will get the nth term for the expansion.