How many square terms are there in the area model of \((a+b+c)^2\)?

Correct answer: 3

The direct answer is B: there are three square terms. In an area model, divide each side of a large square into lengths \(a\), \(b\), and \(c\). A part of length \(a\) meeting another part of length \(a\) forms a square with area \(a^2\). Similarly, the \(b\)-by-\(b\) and \(c\)-by-\(c\) regions have areas \(b^2\) and \(c^2\). Thus the square terms are exactly \(a^2,b^2,c^2\), giving three terms. The full identity is \((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\). Option A is wrong because it misses one of the three variables. Option B is correct because every variable creates one same-by-same square. Option C is wrong because there is no fourth variable or fourth diagonal square. Option D is wrong because six is the number of rectangular cross-term regions, not square regions. Memory cue: count the diagonal regions for square terms; the off-diagonal regions are mixed terms.