Question

Factorise:

$a(a-1)-b(b-1)$

Answer 1

$a(a-1)-b(b-1)$

=$a^2-a-b^2+b$ [Expand the expression]

= $a^2-b^2-a+b$

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

= (a+b)(a-b)-1(a-b)

= (a-b)[(a+b-1)] {taking (a-b) common}