Dear Learners, I present an easy method to solve the given problem.
(a^2-b^2)(c^2-d^2)-4abcd
=a^2(c^2-d^2)-b^2(c^2-d^2)-4abcd, using distributive property in this and the next step
=a^2c^2-a^2d^2-b^2c^2+b^2d^2-4abcd
=a^2c^2+b^2d^2-2abcd-a^2d^2-b^2c^2-2abcd, using commutativity
=(a^2c^2+b^2d^2-2abcd)-(a^2d^2+b^2c^2+2abcd), using (A+B)^2=A^2+2AB+B^2,etc.
=(ac-bd)^2-(ad+bc)^2
=(ac-bd+ad+bc)(ac-bd-ad-bc) Ans.
To arrive at the last step, I used the property A^2-B^2=(A+B)(A-B)
(a^2-b^2)(c^2-d^2)-4abcd
=a^2(c^2-d^2)-b^2(c^2-d^2)-4abcd, using distributive property in this and the next step
=a^2c^2-a^2d^2-b^2c^2+b^2d^2-4abcd
=a^2c^2+b^2d^2-2abcd-a^2d^2-b^2c^2-2abcd, using commutativity
=(a^2c^2+b^2d^2-2abcd)-(a^2d^2+b^2c^2+2abcd), using (A+B)^2=A^2+2AB+B^2,etc.
=(ac-bd)^2-(ad+bc)^2
=(ac-bd+ad+bc)(ac-bd-ad-bc) Ans.
To arrive at the last step, I used the property A^2-B^2=(A+B)(A-B)
Worst not able to understand
ReplyDeleteOnly genious ones can understand as I understood that
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