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).