Which small square must be added to the area model of \(x^2+8x\) to complete a square?

Correct answer: A square of area \(16\)

The correct answer is D: a square of area \(16\). The term \(8x\) can be split into two equal rectangles, each with area \(4x\). These rectangles fit along the sides of an \(x\)-by-\(x\) square, leaving a corner whose side length is 4. To fill that corner, add a square with area \(4^2=16\). The completed model represents \(x^2+8x+16=(x+4)^2\). Option A adds 8, which is the coefficient of \(x\), not the missing square area. Option B has no matching half-coefficient square. Option C squares 8 instead of half of 8 and is too large. Option D correctly follows the complete-square rule: square half the coefficient of the linear term. Memory cue: for \(x^2+bx\), add \((b/2)^2\).