What is the visual result of subtracting the area of a square with side x − 6 from the area of a square with side x + 6?

Correct answer: Four rectangular strips, each with area 6x

Direct answer: A. The required difference is (x + 6)² − (x − 6)². Let a = x + 6 and b = x − 6. The difference-of-squares identity gives a² − b² = (a − b)(a + b). Here, a − b = 12 and a + b = 2x, so the total difference is 12 × 2x = 24x. In a rearranged visual model, this difference can be represented by four congruent rectangular strips, each measuring 6 by x and therefore having area 6x. Their total area is 4 × 6x = 24x. Option A matches both the picture and the calculation. Option B also totals 24x, but it describes eight strips of 3x, which is not the stated model. Option C totals 144, not 24x. Option D totals 24x numerically but describes only two strips of 12x, not the intended four-strip arrangement. Memory cue: when two square areas are subtracted, first try a² − b² = (a − b)(a + b).