A square model has total area (x²+18x+81). If the middle strips are removed and only the two squares remain, what is their total area?

Correct answer: x²+81

Direct answer: Option A, x²+81. Decompose the expression as x²+18x+81=x²+9x+9x+81. In the square model, x² is one square, 81 is the other square, and the two middle strips together have area 18x. Removing the strips leaves x²+81. Option A is correct. Option B, 18x, is precisely the area removed, not the area that remains. Option C incorrectly keeps one strip term together with x² and ignores the separate constant square. Option D confuses 81=9² with 9; the constant square’s area is 81, not 9. Another check is (x+9)²=x²+18x+81, so the two square components are x² and 9²=81. Keep square-tile areas and rectangular-strip areas separate.