(x-4)^2 - 9x^2 = (x-4)(x-4) - 9x^2(x-4)^2 - 9x^2 = (x-4)^2 - (3x)^2(x-4)^2 - 9x^2 = (x-4+3x)(x-4-3x)(x-4)^2 - 9x^2 = (4x-4)(-2x-4)(x-4)^2 - 9x^2 = (-2)(2x-4)(x+2)(x-4)^2 - 9x^2 = -2(2x-4)(x+2)
(x-4)^2 - 9x^2 = (x-4)(x-4) - 9x^2
(x-4)^2 - 9x^2 = (x-4)^2 - (3x)^2
(x-4)^2 - 9x^2 = (x-4+3x)(x-4-3x)
(x-4)^2 - 9x^2 = (4x-4)(-2x-4)
(x-4)^2 - 9x^2 = (-2)(2x-4)(x+2)
(x-4)^2 - 9x^2 = -2(2x-4)(x+2)