You've been told twice
why you can't do that. Please read carefully and think about it. When you distribute, you must only take a factor outside of parentheses themselves: (ax + ay) = a(x + y). You can't take a factor outside of a power; it is not true that (ax)
n = a(x
n).
So it is
not true that (P + Pr)
n simplifies to P(1 + r)
n.
Did you try checking the claim with simple numbers? (I thought you did before.) If P = 100, n = 3, and r = 0.05, then
(P + Pr)n = (100 + 100*0.05)3 = (105)3 = 1,157,625
P(1 + r)n = 100(1 + 0.05)3 = 100(1.05)3 = 100*1.157625 = 115.7625
Those are different. In the first, 100 is inside the parentheses, so it is cubed; in the second, 100 is outside the parentheses and is not cubed.