Which is the correct expansion of ( (a+b)^3 )?

Correct answer: (a^3+3a^2b+3ab^2+b^3)

The direct answer is option B: \\(a^3+3a^2b+3ab^2+b^3\\). The cube means three factors: \\(a+b\\)^3=(a+b)(a+b)(a+b)\\). The binomial cube identity is \\(x+y\\)^3=x^3+3x^2y+3xy^2+y^3\\). Substituting \\(x=a\\) and \\(y=b\\) gives \\(a^3+3a^2b+3ab^2+b^3\\). Option B is correct because it has the two middle terms, both with coefficient 3, and all signs are positive. Option A is wrong because it omits the powers and does not contain the complete middle terms. Option C is the identity for \\(a-b\\)^3\\), so its alternating signs do not fit a sum. Option D contains only the end cubes and leaves out the middle terms. A useful check is to put \\(a=b=1\\): the left side is \\(2^3=8\\), and option B gives \\(1+3+3+1=8\\). Remember: plus-cube has four positive terms with pattern 1, 3, 3, 1.