Which area model represents \(x^2-9\)?

Correct answer: Removing a square of side 3 from a square of side x

The correct answer is A. Since \(9=3^2\), we can write \(x^2-9=x^2-3^2\). The term \(x^2\) is the area of a large square with side x, and \(3^2=9\) is the area of a smaller square with side 3. Removing the smaller square from the larger one leaves exactly the difference \(x^2-9\). B represents \((x+3)^2\), which is a larger square area, not a subtraction. C represents \((x-3)^2=x^2-6x+9\), which contains extra terms and is not equal to \(x^2-9\). D represents an area of \(9x\), not \(x^2-9\). Memory cue: a square’s area is the square of its side, so 9 must be viewed as \(3^2\).