(a²-b²)(c²-d²)-4abcd
Factorise it.
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: (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)]
: (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)]
: (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)]
: (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)]
: (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)]