Question

One of the factor of (a² - b²)(c² - d²) - 4abcd is :

(A) (ac - bd - bc + ad)
(B) ac - bd + bc + ad
(C) Cannot be determined
(D) None of the Above

Answer 1

(a² - b²)( c² - d²) - 4abcd

= {a²c² -a²d² -b²c² + b²d² } -4abcd

= { a²c² + b²d² - 2abcd} -{ a²d² + b²c² +2abcd}

= { (ac)² + (bd)² -2(ac)(bd)} - {(ad)² + (bc)² +2( ad)( bc) }

= ( ac - bd)² - (ad +bc)²

= ( ac - bd + ad + bc)( ac -bd -ad - bc)

Answer 2

Step-by-step explanation:

Given : (a²−b²)(c²−d²)−4abcd

=a²c²−a²d²−b²c²+b²d²−2abcd−2abcd

=a²c²+b²d²−2abcd−a²d²+b²c²−2abcd

=(ac−bd)²−(ad−bc)²

=(ac−bd−ad+bc)(ac−bd+ad−bc) ....Since [p²−q²=(p−q)(p+q)]