What is (9y^2-24y+16) equal to?

Correct answer: ((3y-4)^2)

The direct answer is B: \((3y-4)^2\). Use \((a-b)^2=a^2-2ab+b^2\). The first term \(9y^2\) is \((3y)^2\), and the last term 16 is \(4^2\). Their middle term must be \(-2\cdot3y\cdot4=-24y\), exactly as given. Thus \(9y^2-24y+16=(3y-4)^2\). Option A, \((3y+4)^2\), gives a positive middle term \(+24y\), so the sign is wrong. Option B gives the correct first term, constant term, and negative middle term. Option C, \((9y-4)^2\), has first term \(81y^2\), so it uses the wrong square root. Option D, \((3y-8)(3y-2)\), gives middle terms \(-6y-24y=-30y\) and constant 16, so its middle coefficient is wrong. For such questions, compare all three parts: first square, middle term, and last square. This prevents choosing an answer that matches only two parts.