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Question

Solve (ab+1)2 - (ab)2 where, b - a = 1.
  1. a2 + b2
  2. b2
  3. (a+1)2 + (b+1)2
  4. a2 + (b+1)2


Solution

The correct option is A a2 + b2
(ab+1)2(ab)2=(a(a+1)+1)2(a(a+1))2
=(a2(a+1)2+1+2a(a+1))(a2(a+1)2)
=2a(a+1)+1
=2a2+2a+1
=a2+2a+1+a2
=(a+1)2+a2
=b2+a2 [since b=a+1]

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