Using identity, which form is correct for ( (7+3)^2 )?

Correct answer: (7^2+2\cdot7\cdot3+3^2)

The direct answer is option B: \((7+3)^2=7^2+2\cdot7\cdot3+3^2\). Use the identity \((a+b)^2=a^2+2ab+b^2\). Here \(a=7\) and \(b=3\), so substitute them in order: first square is \(7^2\), the middle term is positive \(2\cdot7\cdot3\), and the last square is \(3^2\). Numerically this is \(49+42+9=100\), matching \(10^2\). Option A has a negative middle term, which belongs to \((a-b)^2\), not a plus sign. Option B has the exact required pattern and is correct. Option C, \(7^2-3^2\), is a difference of squares and does not equal a square of a sum. Option D omits the cross term \(2ab\), so it is incomplete. Memory cue: plus inside the bracket means plus in the middle term; minus means minus.