A square visual model first has side a. A strip of width b is added on the right and another strip of width b is added at the bottom, creating a small corner square. Which identity does the total area represent?

Correct answer: a² + 2ab + b² = (a + b)² — a² + 2ab + b² = (a + b)²

The direct answer is A: a² + 2ab + b² = (a + b)². Begin with the original square, whose area is a². The strip on the right has dimensions a by b, so its area is ab. The strip at the bottom also has area ab because it has the same dimensions. The little corner is a b by b square, so its area is b². Adding all non-overlapping parts gives a² + ab + ab + b² = a² + 2ab + b². These pieces together form a larger square with side a+b, whose area is (a+b)². B describes a difference of squares, not an enlarged square. C is used when widths are removed, so its middle term is negative. D counts only one ab strip and therefore misses part of the area. Memory cue: adding the same width to both sides gives plus 2ab.