Which expansion is correct in the area model of a square with side (3p-4)?

Correct answer: 9p^2-24p+16

Direct answer: A. The area of a square is side multiplied by itself, so the required expression is (3p-4)^2. Apply (u-v)^2=u^2-2uv+v^2 with u=3p and v=4. The first square is (3p)^2=9p^2. The two equal negative rectangles together have area -2(3p)(4)=-24p. The small square has area 4^2=16. Adding these signed parts gives 9p^2-24p+16. Option B misses the factor 2 and therefore gives the wrong middle coefficient. Option C treats (3p)^2 as 3p^2 instead of 9p^2. Option D has the wrong sign; subtraction in the side creates a negative middle term. The area model shows one large positive square, two negative rectangles, and one positive small square. Memory cue: square each end and use twice the product in the middle, keeping the sign from the binomial.