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In an area model of a square of side \(a\), two \(ab\) rectangles are removed and their common \(b^2\) part is added back once. Which identity does this visual model represent?
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Answer and explanation
Correct answer: \((a-b)^2=a^2-2ab+b^2\)
Removing two \(ab\) rectangles gives \(a^2-ab-ab\). Their overlap \(b^2\) was subtracted twice, so add it once: \(a^2-2ab+b^2\). Exam tip: removal in an area model indicates a negative term.
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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?
Removing two \(ab\) rectangles gives \(a^2-ab-ab\). Their overlap \(b^2\) was subtracted twice, so add it once: \(a^2-2ab+b^2\). Exam tip: removal in an area model indicates a negative term.
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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