What is the correct expansion of the identity ( (a+b)^2 )?

Correct answer: (a^2+2ab+b^2) / correct expansion

The square of a sum contains three parts: the square of the first term, twice the product of the two terms, and the square of the second term. In algebraic form, the identity is \\(a+b\\)^2=a^2+2ab+b^2. The middle term appears because the two cross-products, \(ab\) and \(ba\), are equal and together make \(2ab\).

Applying this identity gives the expansion \(a^2+2ab+b^2\), so option B is correct. For example, if both terms are added and the result is multiplied by itself, the products are \(a^2\), \(ab\), \(ba\), and \(b^2\). The two middle products combine to \(2ab\). Option A omits these products, while option C gives the wrong sign and option D is not a square expansion.