What is the sum of the four parts in the rectangle model of (x+2)(x+5)?

Correct answer: x²+7x+10

The direct answer is A: x²+7x+10. Draw or imagine a rectangle with one side split into x and 2 and the other side split into x and 5. The four smaller regions have areas x×x=x², x×5=5x, 2×x=2x, and 2×5=10. Adding all regions gives x²+5x+2x+10=x²+7x+10. Option A combines the like terms correctly. Option B uses 10 as the coefficient of x and 7 as the constant, confusing the sum of 2 and 5 with their product. Option C uses 3x, which is only (2+1)x and does not represent the two cross-products. Option D has the correct x coefficient but changes the constant 10 to 7. A useful check is (x+m)(x+n)=x²+(m+n)x+mn; here m+n=7 and mn=10.