In a square of side (x+2), a square of side (x-2) is placed at a corner. How will the remaining outer area be expressed?

Correct answer: 8x / remaining area

The correct answer is A: 8x. The remaining outer area is the area of the large square minus the area of the smaller square: (x+2)^2-(x-2)^2. Apply the difference-of-squares identity with P=x+2 and Q=x-2. The result is [(x+2)-(x-2)] [(x+2)+(x-2)] = 4×2x=8x. Visually, the leftover region consists of two strips around the smaller square. Each strip has width 4, while their combined length contribution gives the same total area 8x; the identity is the safest calculation. Option A is correct. Option B, 4x, describes only half of the total strip area in this comparison. Option C is the product (x+2)(x-2)=x^2-4, not the difference of the square areas. Option D is only a constant and ignores the variable length x. Memory cue: when one square is inside another, subtract their areas, then use difference of squares rather than expanding unnecessarily.