Which visual partition is correct for (r + 2)²?

Correct answer: r², 2r, 2r, and 4

The correct answer is A: r², 2r, 2r, and 4. A square with side r + 2 can be partitioned into a large r by r square, two rectangles each measuring r by 2, and a small 2 by 2 corner square. Their areas are r², 2r, 2r, and 4. Adding them gives r² + 2r + 2r + 4 = r² + 4r + 4, which is the expansion of (r + 2)². Option B leaves out one of the two equal strips, so it gives too little area. Option C doubles each strip incorrectly: an r by 2 strip has area 2r, not 4r. Option D uses negative strip areas, but the 2 units are added to the side, so the strips must have positive areas. The corner is 2² = 4. Memory cue: for (a + b)², the visual pieces are a², ab, ab, and b²; there are always two middle rectangles.