What is the simplified form of ( (3a+4b)(3a-4b) )?

Correct answer: \(9a^2-16b^2\)

The direct answer is option D: \(9a^2-16b^2\). Start with the identity \((x+y)(x-y)=x^2-y^2\). Here, the common first term is \(x=3a\), and the second term is \(y=4b\). Therefore, \((3a+4b)(3a-4b)=(3a)^2-(4b)^2=9a^2-16b^2\). Option A has a plus sign, but opposite signs in the brackets produce a difference of squares, not a sum. Option B incorrectly changes the coefficients and powers. Option C is the expansion of a form such as \((3a-4b)^2\), so it includes a middle term that cancels here. Option D correctly gives the difference of the two squares. Memory cue: same terms with opposite signs mean square the first term minus square the second term.