Let's expand the left side of the equation first:

(x+1)(x-1) = x^2 - 1

Now, let's expand the right side of the equation:

(x+2)^2 = (x+2)(x+2) = x^2 + 4x + 4

So, the equation becomes:

x^2 - 1 = x^2 + 4x + 4

Now, let's simplify:

x^2 - 1 = x^2 + 4x + 4
0 = 4x + 5

This equation does not hold true, so the original statement that (x+1)(x-1) = (x+2)^2 is incorrect.