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Question

Which of the given options is an algebraic identity?
  1. a+2=3+b
  2. (a+b)(ab)=a2b2
  3. a+6=a2
  4. 4b=b


Solution

The correct option is B (a+b)(ab)=a2b2
a+2=3+b holds true for values like a=4 and b=3 or a=2 and b=1. But this equation is not true for any value of a and b. For example, this equation does not hold true when a=1 and b=2. So, the equation a+2=3+b is not an identity.

Similarly a+6=a2 is true for a=3 but not true for a=4.
Hence the equation a+6=a2 is also not an identity.

Also, 4b=b is true only when b=2.
Hence 4b=b is not an identity.

But the equation (a+b)(ab)=a2b2 holds true for any value of a and b.
Hence this is an identity.

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