Which structure must an expression have to be factorised using the identity for the difference of squares?

Correct answer: Difference of two perfect-square terms, \(A^2-B^2\)

Direct answer: A, a difference of two perfect squares, \(A^2-B^2\). The identity is \(A^2-B^2=(A-B)(A+B)\). It requires two terms, each of which is a perfect square, separated by a minus sign. For example, \(x^2-9=x^2-3^2=(x-3)(x+3)\). Option B has a plus sign; the expression \(A^2+B^2\) is not factored by the difference-of-squares identity. Option C has three terms and does not have the required two-square structure. Option D is a difference of cubes, not squares; it belongs to a different identity, \(A^3-B^3=(A-B)(A^2+AB+B^2)\). A frequent confusion is to focus only on the minus sign and forget that both terms must also be squares. Memory cue: “square minus square gives difference times sum.”