UGC NET Questions (Paper – 1)

This option is correct because the expansion of (a + b)² gives a² + 2ab + b². We obtain this by multiplying (a + b)(a + b) and collecting like terms. The cross terms ab and ba combine to give 2ab. Therefore, the complete identity is (a + b)² = a² + 2ab + b².

Option A:
The expression a² + b² omits the middle term 2ab that arises from the cross products in the expansion. It would represent (a − b)² only if combined with a negative cross term, but as written it is incomplete. Hence, it is not the correct identity here.

Option B:
The expression a² − 2ab + b² is the expansion of (a − b)², not (a + b)². The negative sign on 2ab indicates subtraction rather than addition. Therefore, this identity does not match the given binomial square.

Option C:
The expression a² + 2ab + b² correctly represents the square of a sum. It includes the squares of both terms and twice their product. This matches the standard algebraic identity for (a + b)², so this option is correct.

Option D:
The expression 2a² + b² does not arise from any simple binomial square formula. It has an incorrect coefficient on a² and is missing the cross term. Thus, it cannot represent (a + b)².