What will be the expansion of ( (3a+b)^2 )?

Correct answer: (9a^2+6ab+b^2)

The identity \\(p+q)^2=p^2+2pq+q^2\\) helps expand a square of two terms. Here, the first term is \\(3a\\) and the second term is \\(b\\). Therefore, the expansion must contain the square of \\(3a\\), a middle term involving both terms, and the square of \\(b\\). This structure is important because the plus sign between the terms makes the middle term positive.

Substituting gives \\((3a+b)^2=(3a)^2+2(3a)(b)+b^2\\). Now, \\((3a)^2=9a^2\\) and \\(2(3a)(b)=6ab\\). Hence the result is \\(9a^2+6ab+b^2\\), which is option A. Option C misses the middle term, while option D has the wrong sign.