(x - 1)(x + 1) - (x - 3)^2 = x^2 - 1 - (x^2 - 6x + 9) = x^2 - 1 - x^2 + 6x - 9 = x^2 - x^2 + 6x - 1 - 9 = 6x - 10.
(x - 1)(x + 1) - (x - 3)^2 = x^2 - 1 - (x^2 - 6x + 9) = x^2 - 1 - x^2 + 6x - 9 = x^2 - x^2 + 6x - 1 - 9 = 6x - 10.