A rectangle model is formed by (3x+2) and (3x-2). What will be the area?
Answer and explanation
Correct answer: \(9x^2-4\)
The area of the rectangle is the product of its side lengths: \((3x+2)(3x-2)\). It has the form \((a+b)(a-b)=a^2-b^2\), where \(a=3x\) and \(b=2\). Hence, the area is \((3x)^2-2^2=9x^2-4\). \(9x^2+4\) incorrectly uses the sum of squares; this identity requires their difference. Exam tip: when matching binomials have opposite signs, apply the difference-of-squares identity directly.
Frequently asked questions
What is the correct answer to this question?
\(9x^2-4\)
Why is this the correct answer?
The area of the rectangle is the product of its side lengths: \((3x+2)(3x-2)\). It has the form \((a+b)(a-b)=a^2-b^2\), where \(a=3x\) and \(b=2\). Hence, the area is \((3x)^2-2^2=9x^2-4\). \(9x^2+4\) incorrectly uses the sum of squares; this identity requires their difference. Exam tip: when matching binomials have opposite signs, 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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