Factorise the following:

(x - y)² - 9

(x - y)² - 9 = (x - y)² - (3)².

Using identity,

a² - b² = (a + b)(a - b).

(x - y)² - (3)² = (x - y + 3)(x - y - 3).

Hence, (x - y)² - 9 = (x - y + 3)(x - y - 3).