In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?

Correct answer: \((a^2+2ab+b^2)\)

The correct answer is B: the total area is \(a^2+2ab+b^2\), equal to \((a+b)^2\). A square with side \(a+b\) has area \((a+b)(a+b)\). The perpendicular cuts divide its sides into lengths \(a\) and \(b\), producing four regions: an \(a\)-by-\(a\) square with area \(a^2\), two \(a\)-by-\(b\) rectangles with areas \(ab\) each, and a \(b\)-by-\(b\) square with area \(b^2\). Their sum is \(a^2+ab+ab+b^2=a^2+2ab+b^2\). A lists only the two corner squares and leaves out both rectangles. C represents a difference of squares and would involve subtraction, not a complete partition into positive areas. D is a perimeter-type expression, not an area expression. The slash in the options is understood as separating the bilingual form, not as division. Memory cue: area of the whole equals the sum of every non-overlapping part.