In the first solution, we wrote T(n) = 4T(n-1)+8, but we could just write T(n) = 4T(n-1)+1, because 8 is a constant, it's in O(1)

In the second solution, we directly took n4^n as the greatest term, but we can be more precise, we can notice that we have the sum of k4^k with k from 1 to n, we get:

But the final result remains the same