In a rectangle model, the sides are \(s+3\) and \(s-3\). Which area is correct?

Correct answer: \(s^2-9\)

The correct answer is A: \(s^2-9\). The area of a rectangle is the product of its length and breadth, so multiply \((s+3)(s-3)\). This is the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\), with \(a=s\) and \(b=3\). Therefore, the area is \(s^2-3^2=s^2-9\). If expanded directly, \(s^2-3s+3s-9\) results; the two middle terms cancel, leaving \(s^2-9\). Option B has the wrong sign for the constant term. Options C and D are expansions of \((s-3)^2\) and \((s+3)^2\), respectively; those are squares of one binomial, not the product of conjugate binomials in the question. A helpful memory cue is that equal opposite additions and subtractions cancel the middle terms, and the remaining result is the first square minus the second square. Thus the rectangle area is uniquely option A.