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Assume that \(x>y\). Which rectangle can directly represent \(x^2-y^2\) as an area?
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Answer and explanation
Correct answer: A rectangle with length \(x+y\) and breadth \(x-y\)
The rectangle’s area is \((x+y)(x-y)\). Using the identity, \((x+y)(x-y)=x^2-y^2\), so A is correct. Option D has area \((x+y)^2\). Exam tip: conjugate binomials produce a difference of squares.
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What is the correct answer to this question?
A rectangle with length \(x+y\) and breadth \(x-y\)
Why is this the correct answer?
The rectangle’s area is \((x+y)(x-y)\). Using the identity, \((x+y)(x-y)=x^2-y^2\), so A is correct. Option D has area \((x+y)^2\). Exam tip: conjugate binomials produce a 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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