Choose the correct expansion of ( (3a-4b)^2 ).

Correct answer: (9a^2-24ab+16b^2)

The direct answer is option A: 9a^2 - 24ab + 16b^2. Use the identity (x - y)^2 = x^2 - 2xy + y^2. Put x = 3a and y = 4b. Then (3a - 4b)^2 = (3a)^2 - 2(3a)(4b) + (4b)^2 = 9a^2 - 24ab + 16b^2. Option A is correct because all three parts—the first square, the negative double product and the second square—are calculated correctly. Option B has +24ab, but the middle term must be negative because the binomial contains subtraction. Option C incorrectly gives 3a^2 instead of 9a^2 and 4b^2 instead of 16b^2; coefficients must be squared. Option D, 9a^2 - 16b^2, is a difference of squares and leaves out the middle term, so it is not the square of a difference. A useful check is to multiply directly: (3a - 4b)(3a - 4b) gives 9a^2 - 12ab - 12ab + 16b^2, and the middle terms combine to -24ab. Memory cue: square the first, subtract twice their product, square the second.