Factorise the following:

a(a - 2) - b(b - 2)

a(a - 2) - b(b - 2) = a² - 2a - b² + 2b

= a² - b² - 2a + 2b

= (a - b)(a + b) - 2(a - b)

= (a - b)(a + b - 2).

Hence, a(a - 2) - b(b - 2) = (a - b)(a + b - 2).