Question

Factorise the following:

(a² – b²)(c² – d²) – 4abcd

Answer 1

(a² – b²)(c² – d²) – 4abcd

= a²c² – a²d² – b²c² + b²d² – 4abcd

= a²c² + b²d² – 2abcd – a²d² – b²c² – 2abcd

= (a²c² + b²d² – 2abcd) – (a²d² + b²c² + 2abcd)

= (ac – bd)² – (ad + bc)²

= [(ac – bd) + (ad + bc)][(ac – bd) – (ad + bc)]

= (ac – bd + ad + bc)(ac – bd – ad – bc).