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Question

Solve (ab+1)2 - (ab)2 where, b - a = 1.


A

a2 + b2

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B

a2 + (b+1)2

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C

(a+1)2 + (b+1)2

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D

b2

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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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