In the visual model of (r + s)(r − s), why do the middle terms disappear?

Correct answer: Because they are equal in magnitude and have opposite signs

The correct answer is A: the middle terms are equal in magnitude and have opposite signs. Multiply the two binomials term by term: (r + s)(r − s) = r·r + r·(−s) + s·r + s·(−s) = r² − rs + rs − s². The two middle terms are −rs and +rs. They represent equal areas or products with opposite signs, so their sum is zero: −rs + rs = 0. What remains is r² − s². In a visual model, one middle rectangular region can be viewed as a positive rs area and the other as a negative rs area; they cancel each other. B is incorrect because r² is generally not zero. C is incorrect because s² is the final negative term, not the reason the middle terms cancel. D is incorrect because cancellation depends on opposite signs, not on the two side lengths being equal. The key memory cue is that conjugate factors, (r+s) and (r−s), always create opposite middle products. This gives the identity (r+s)(r−s)=r²−s².