If (6²−2²) is changed into a visual rectangle, what will the dimensions be?

Correct answer: (6+2) and (6−2)

The direct answer is A: dimensions 6+2 and 6−2, which are 8 and 4. The difference-of-squares identity says a²−b²=(a+b)(a−b). Substituting a=6 and b=2 gives 6²−2²=(6+2)(6−2)=8×4=32. Direct calculation also gives 36−4=32, confirming the same area. B gives dimensions 6 and 2, whose area is only 12, so it does not represent the difference of squares. C gives 12 and 4, whose product is 48 and incorrectly doubles both original numbers. D gives 4 and 4, whose area is 16 and omits the required sum factor. Thus A is the only pair that preserves the original area. Memory cue: subtracting two squares becomes a rectangle whose sides are the sum and the difference of the square roots.