Which visual comparison can find (101^2-99^2) immediately?

Correct answer: (101-99)(101+99) / difference-of-squares rectangle

The correct answer is A: (101-99)(101+99). The difference-of-squares identity is P^2-Q^2=(P-Q)(P+Q). Taking P=101 and Q=99 gives 101^2-99^2=(101-99)(101+99)=2×200=400. In a visual comparison, the larger square and the smaller square overlap; the remaining strips can be rearranged into a rectangle whose sides are the difference and the sum of the original side lengths. Option A represents exactly this rectangle. Option B calculates only the square of the difference, 2^2=4, which is not the difference of the two large square areas. Option C adds the areas instead of subtracting them. Option D is the product of the side lengths and is not equal to the difference of their squares. A useful mental shortcut is to centre the numbers around 100: 101^2-99^2=(100+1)^2-(100-1)^2=4×100×1=400. Memory cue: difference of nearby squares is often much faster as difference times sum.