Assume that \(a>b\). In the area model of \(a^2-b^2=(a+b)(a-b)\), after removing the smaller square from the larger square and rearranging the remaining pieces, which rectangle is formed?
Answer and explanation
Correct answer: A rectangle with sides \(a+b\) and \(a-b\)
The large square has area \(a^2\), while the removed small square has area \(b^2\). Rearranging the leftover pieces gives a rectangle with sides \((a+b)\) and \((a-b)\). \((a-b)^2\) misses the conjugate factor \((a+b)\). Exam tip: recognise difference of squares as conjugate factors.
Frequently asked questions
What is the correct answer to this question?
A rectangle with sides \(a+b\) and \(a-b\)
Why is this the correct answer?
The large square has area \(a^2\), while the removed small square has area \(b^2\). Rearranging the leftover pieces gives a rectangle with sides \((a+b)\) and \((a-b)\). \((a-b)^2\) misses the conjugate factor \((a+b)\). Exam tip: recognise difference of squares as conjugate factors.
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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