one of the factors of (a2-b2) (c2-d2) -4abcd is a)(ac-bd+bc+ad) b)ac+bd+bc+ad c)ab+bd-bc-ad explain andd then give your answer - Maths - Factorisation

Question

one of the factors of (a2-b2)
(c2-d2) -4abcd is
a)(ac-bd+bc+ad)
b)ac+bd+bc+ad
c)ab+bd-bc-ad
explain andd then give your answer

Ajanta Trivedi · Accepted Answer

the given expression is:
(a2-b2)(c2-d2)-4abcd=a2c2-b2c2-a2d2+b2d2-4abcd=a2c2+b2d2-2abcd-b2c2-a2d2-2abcd =(ac)2+(bd)2-2ac
bd-(bc)2+(ad)2+2bc
ad  [since (A±B)2=A2+B2±2AB=ac-bd2-bc+ad2    [since A2-B2=(A-B)(A+B)=ac-bd+bc+adac-bd-bc-ad

thus (ac-bd+bc+ad) is the factor of the given expression
thus option (a) is correct

hope this helps you

one of the factors of (a2-b2) (c2-d2) -4abcd is a)(ac-bd+bc+ad) b)ac+bd+bc+ad c)ab+bd-bc-ad explain andd then give your answer.

one of the factors of (a²-b²) (c²-d²) -4abcd is

a)(ac-bd+bc+ad)

b)ac+bd+bc+ad

c)ab+bd-bc-ad

explain andd then give your answer.