Question

# Which of the given options is an algebraic identity?a+2=3+b(a+b)(a−b)=a2−b2a+6=a24−b=b

Solution

## The correct option is B (a+b)(a−b)=a2−b2a+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, 4−b=b is true only when b=2. Hence 4−b=b is not an identity. But the equation (a+b)(a−b)=a2−b2 holds true for any value of a and b. Hence this is an identity.

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