Which expansion shows the full area of a square with side \(a+b+c\)?

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

The direct answer is B. The area of the large square is side multiplied by itself: \((a+b+c)^2\). In the visual grid there are three diagonal squares, with areas \(a^2\), \(b^2\), and \(c^2\). There are also six off-diagonal rectangles: two of area \(ab\), two of area \(bc\), and two of area \(ca\). Adding all parts gives \(a^2+b^2+c^2+2ab+2bc+2ca\). A includes only one rectangle for each pair and therefore misses half of the cross area. C uses negative cross terms, which would correspond to a different arrangement involving subtraction. D introduces \(abc\), a cubic term, but a square area from these side lengths has total degree two and contains no triple product. Memory cue: every pair among a, b, c appears twice in the grid.