Using an algebraic identity, what is the area of a square with side \(20-1\)?

Correct answer: \(361\)

The correct answer is B: \(361\). A square's area is the square of its side, so the required area is \((20-1)^2\). Apply \((a-b)^2=a^2-2ab+b^2\): \((20-1)^2=20^2-2(20)(1)+1^2=400-40+1=361\). Direct checking gives \(19^2=361\). Option A, 399, comes from incorrectly doing only \(400-1\); the middle term \(-2ab\) cannot be omitted. Option C, 381, does not follow from the identity or direct squaring. Option D, 421, uses the wrong sign or adds instead of subtracting the cross-term. The visual model also shows why the area is not simply the large square minus one unit: two rectangular strips must be removed, and the corner unit must be restored. Memory cue: in \((a-b)^2\), subtract twice the product and then add \(b^2\).