In the visual model of \(49^2\), using \((50-1)^2\), which is the small square?

Correct answer: \(1^2\)

The correct answer is C, \(1^2\). Begin with the identity \((a-b)^2=a^2-2ab+b^2\). Here, \(a=50\) and \(b=1\). In the visual square model, the large square has side 50, while the part removed from each side has width 1. The small corner formed by the removed strips is a square whose side is 1, so its area is \(1\times1=1^2\). Option A, \(50^2\), is the area of the original large square. Option B, \(49^2\), is the area of the final square whose side is 49, not the small corner square. Option D, \(2\times50\times1\), represents the combined area of two rectangular strips in the model, not the small square. Memory cue: in \((a-b)^2\), the small square has area \(b^2\), while the two strips together have area \(2ab\).