Confused with factorising a maths problem?

Question

How do you get from ((3^k)-1 + 2*3^k)/2 to ((3*3^k)-1)/2? When i factorise i get ((3^k*3^k)-1)/2 but this is not the correct answer, please explain the steps i need to take in achieving the above mentioned

Answer 1

Just replace 3^k with N for a second.

(N - 1 + 2N) / 2

Can you see it now?
(3N - 1) / 2

Substitute back in:
((3* 3^k) - 1 ) / 2


In side the parentheses you have 3^k and then 2*3^k. This adds together to be 3*3^k. And you still have the -1.