Hello StackExchange world,

While doing a proof, I encountered:
$$ 
= S(n-1)+3^n-3^{n-1}
$$

I am focused on the latter part, with the powers of n, apparently it reduces after factoring to:

$$
2\*3^{n-1}
$$

and I have no idea why. I tried thinking of n as a concrete number, and then n-1 the one before that, and I still can't wrap my mind around it. I am hoping someone can enlighten me here. Thank you all for the time and effort.