Which model shows \(a^2+2ab+b^2\) as a complete square?

Correct answer: Square of side \(a+b\)

The direct answer is C: a square with side \(a+b\). Start with the identity \((a+b)^2=a^2+2ab+b^2\). A square whose side is split into lengths \(a\) and \(b\) in both directions contains one \(a^2\) square, one \(b^2\) square, and two rectangles of area \(ab\). Adding these regions gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Therefore option C matches the complete square exactly. Option A represents \((a-b)^2=a^2-2ab+b^2\), so its middle term has the wrong sign. Option B shows only \(a^2+b^2\) and misses the two cross-regions. Option D represents a product \((a+b)(a-b)=a^2-b^2\), not the given expression. Memory cue: plus \(2ab\) means the sum square; minus \(2ab\) means the difference square.