In which rearrangement is the area (a^2-b^2) shown as the rectangle ((a+b)(a-b))?

Correct answer: Removing a square of side (b) from a square of side (a) and making a rectangle

Direct answer: B. A square of side a has area a^2, and a smaller square of side b has area b^2. Removing the smaller square leaves the region a^2-b^2. If the remaining pieces are cut and rearranged without changing their total area, they form a rectangle whose two side lengths are a+b and a-b. Its area is therefore (a+b)(a-b), proving the identity a^2-b^2=(a+b)(a-b). Option A concerns partitioning a different complete square and does not specifically create the difference-of-squares remainder. Option B describes both the subtraction and the rearrangement needed. Option C produces the addition pattern associated with a binomial square. Option D only joins line segments; line lengths alone do not establish an area identity. A reliable memory cue is: remove the small square first, then rearrange the leftover pieces into a rectangle; the rectangle’s sides are the sum and difference of the original side lengths.