find the first 3 terms in the expansion of (x+4)(1+3x)^-2 as a series in ascending powers.

Question

I expanded the second bracket using binomial expansion and got 1 -6x +27x^2 -108x^3

how do I combine (x+4) with the expansion?

Any help would be appreciated.

Answer 1

just multiply out as usual, taking only the firet 3 terms:

(1 -6x +27x^2 -108x^3)(4+x)
= (1 -6x +27x^2 -108x^3)*4
+ (1 -6x +27x^2 -108x^3)*x

= 4 - 24x + 108x^2 - ...
+ x - 6x^2 + 27x^3 - ...
----------------------------------
4 - 23x + 102x^2 + ...