What is the visual area expression of a square with side (n-2)?
Answer and explanation
Correct answer: \(n^2-4n+4\)
The area of a square is the square of its side. Therefore, for side \((n-2)\), the area is \((n-2)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=n\) and \(b=2\), we get \(n^2-2(n)(2)+2^2=n^2-4n+4\). The expression \(n^2-4\) is not the square of a difference; it equals \((n-2)(n+2)\). Exam tip: in \((a-b)^2\), the middle term is always negative, \(-2ab\).
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What is the correct answer to this question?
\(n^2-4n+4\)
Why is this the correct answer?
The area of a square is the square of its side. Therefore, for side \((n-2)\), the area is \((n-2)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=n\) and \(b=2\), we get \(n^2-2(n)(2)+2^2=n^2-4n+4\). The expression \(n^2-4\) is not the square of a difference; it equals \((n-2)(n+2)\). Exam tip: in \((a-b)^2\), the middle term is always negative, \(-2ab\).
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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