In a rectangle model, (x + 2) and (x + 5) are replaced by (x + 3) and (x + 4). What is the difference between the two areas?

Correct answer: 2

The direct answer is A: the difference between the areas is 2. The original rectangle has area (x + 2)(x + 5). Multiplying gives x² + 7x + 10. The new rectangle has area (x + 3)(x + 4), which gives x² + 7x + 12. Subtract the original area from the new area: (x² + 7x + 12) − (x² + 7x + 10) = 2. The x² terms cancel and the 7x terms also cancel, so only the constant difference remains. Option A is correct because the new area is exactly 2 square units greater. Option B is wrong because the constant terms 12 and 10 are not equal. Option C is wrong because the x terms cancel rather than leaving x. Option D is wrong because no 2x term remains after subtraction. A useful check is to notice that the two products have the same sum of factors, 7x, but their constant products are 10 and 12. Memory cue: when comparing expanded expressions, combine like terms and cancel identical terms carefully.