A rectangle has sides (2x+1) and (2x-1). What area is obtained from the visual model?
Answer and explanation
Correct answer: \(4x^2-1\)
The area of a rectangle is the product of its side lengths: \((2x+1)(2x-1)\). This matches \((a+b)(a-b)=a^2-b^2\), where \(a=2x\) and \(b=1\). Hence, the area is \((2x)^2-1^2=4x^2-1\). The expression \(4x^2+1\) does not apply the difference-of-squares identity correctly. Exam tip: when two binomials differ only in the middle sign, look for the difference of squares.
Frequently asked questions
What is the correct answer to this question?
\(4x^2-1\)
Why is this the correct answer?
The area of a rectangle is the product of its side lengths: \((2x+1)(2x-1)\). This matches \((a+b)(a-b)=a^2-b^2\), where \(a=2x\) and \(b=1\). Hence, the area is \((2x)^2-1^2=4x^2-1\). The expression \(4x^2+1\) does not apply the difference-of-squares identity correctly. Exam tip: when two binomials differ only in the middle sign, look for the difference of squares.
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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