prove that (3x+1)^2 - (3x-1)^2 is a multiple of 4 for all positive integer values of x

(3x + 1)² = 9x² + 6x + 1 (3x - 1)² = 9x² - 6x + 1 (9x² + 6x + 1) - (9x² - 6x + 1) = 12x 12x/4 = 3x Therefore for all positive integers of x the result is a multiple of 4