Which model gives the most direct visual explanation of \((a+b)(a-b)=a^2-b^2\)?

Correct answer: Removing a square of side \(b\) from a square of side \(a\) and rearranging the remainder into a rectangle

The correct answer is A. Begin with a large square of side \(a\), whose area is \(a^2\), and remove a smaller square of side \(b\), whose area is \(b^2\). The remaining L-shaped region has area \(a^2-b^2\). By cutting and rearranging that remainder without changing its area, it can form a rectangle whose side lengths are \(a+b\) and \(a-b\). Its area is therefore \((a+b)(a-b)\), proving the identity visually. B does not identify the two square areas or the required rearrangement. C adds \(a^2\) and \(b^2\), whereas the identity requires their difference. D starts with the wrong square relationship and does not produce the factors \(a+b\) and \(a-b\). The important principle is conservation of area: cutting and rearranging changes shape, not total area. Memory cue: difference of squares becomes a rectangle after cut-and-rearrange.