Question

Factorise the following by the difference of two squares:
a(a - 1) - b(b - 1)

Answer 1

a(a - 1) - b(b - 1)
 a² - a - b² + b
= a² - b² - a + b
= (a² - b²) - (a - b)
= (a - b)(a + b) - (a - b)
= (a - b)(a + b - 1).