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In an area model of a square with side \(a\), strips of width \(b\) are removed along two adjacent sides. The common \(b\times b\) corner is added once to correct for being removed twice. Which identity does this model represent?
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Answer and explanation
Correct answer: \((a-b)^2=a^2-2ab+b^2\)
The two strips have total area \(ab+ab=2ab\), but their \(b^2\) corner is subtracted twice. Hence the remaining area is \(a^2-2ab+b^2=(a-b)^2\). Exam tip: add back the overlapping region once.
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What is the correct answer to this question?
\((a-b)^2=a^2-2ab+b^2\)
Why is this the correct answer?
The two strips have total area \(ab+ab=2ab\), but their \(b^2\) corner is subtracted twice. Hence the remaining area is \(a^2-2ab+b^2=(a-b)^2\). Exam tip: add back the overlapping region once.
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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