In the model of a square with side (5p−2q), what will the corner term and the middle area be, respectively?

Correct answer: 4q² and −20pq; corner and middle terms

Correct answer: C. Use the square identity (u−v)²=u²−2uv+v² with u=5p and v=2q. The corner associated with the q-part is v²=(2q)²=4q². The two middle rectangles together have area −2(5p)(2q)=−20pq, because the minus sign in the side makes both cross regions negative in the algebraic model. Option A forgets to square 2q, so it gives a length rather than a corner area. Option B halves both required contributions and therefore does not represent the complete pair of middle rectangles. Option D wrongly makes the square of 2q negative; an ordinary square term is positive, while the middle term keeps the negative sign. A useful memory cue is “corner means square, middle means twice the product.”