Question

Factorise : (a^2-b^2)(c^2-d^2)-4abcd​

Answer 1

Step-by-step explanation:

Hi there,

Solution:-

(a^2-b^2)(c^2-d^2)-4abcd

a²c²-a²d²-b²c²+b²d²-4abcd

a²c²-a²d²-b²c²+b²d²-2abcd-2abcd

a²c²+b²d²-2abcd-a²d²-b²c²-2abcd

(a²c²+b²d²-2abcd)-(a²d²+b²c²+2abcd)

[(ac)²+(bd)²-2abcd]-[(ad)²+(bc)²+2abcd]

We know that,

[x²+y²-2xy=(x-y)²] and

[x²+y²+2xy=(x+y)²]

=>(ac−bd)²−(ad+bc)²

We know that,

[(a²-b²)=(a+b)(a-b)]

=>[ac-bd+(ad+bc)][ac−bd)−(ad+bc)]

=>(ac-bd+ad+ac)(ac-bd-ad-bc) ANSWER...

Hope this helps you:-)