In a rectangle model, the sides are (s+3) and (s-3). Which area is correct?
Answer and explanation
Correct answer: \(s^2-9\)
The area of the rectangle is the product of its sides: \((s+3)(s-3)\). Using the identity \((a+b)(a-b)=a^2-b^2\), the area is \(s^2-3^2=s^2-9\). Although \(s^2+9\) also has no middle term, its constant term has the wrong sign. Exam tip: whenever you see \((a+b)(a-b)\), apply the difference-of-squares identity directly.
Frequently asked questions
What is the correct answer to this question?
\(s^2-9\)
Why is this the correct answer?
The area of the rectangle is the product of its sides: \((s+3)(s-3)\). Using the identity \((a+b)(a-b)=a^2-b^2\), the area is \(s^2-3^2=s^2-9\). Although \(s^2+9\) also has no middle term, its constant term has the wrong sign. Exam tip: whenever you see \((a+b)(a-b)\), apply the difference-of-squares identity directly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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