If 9^2-4^2 is solved using a visual model, which rectangle is formed?

Correct answer: A rectangle with dimensions 9+4 and 9-4

The direct answer is A. Use the difference-of-squares identity a^2-b^2=(a+b)(a-b). Substituting a=9 and b=4 gives 9^2-4^2=(9+4)(9-4)=13×5. In a visual model, a 9-by-9 square and a 4-by-4 square are compared; the remaining pieces can be rearranged to form one rectangle with side lengths 9+4 and 9-4. A therefore describes the resulting rectangle. B gives 9×4, which is a product of the original side lengths, not the difference of their square areas. C gives dimensions 18 and 8, whose product is 144 and does not equal 65. D gives a 5-by-5 square, not the rearranged rectangle, and its area is 25. A numerical check confirms the result: 81-16=65 and 13×5=65. Memory cue: difference of two squares becomes a sum times a difference—plus first, minus second.