Which expansion is given by the area model of a square with side (k-4)?
Answer and explanation
Correct answer: \(k^2-8k+16\)
The area of a square is the square of its side. Thus, \((k-4)^2=k^2-2\cdot k\cdot4+4^2=k^2-8k+16\). In the area model, two rectangular parts of area \(4k\) are removed from the \(k^2\) region, and the corner square of area \(16\) is added. Option A has only \(-4k\) as the middle term, but it should be \(-8k\). Exam tip: in \((a-b)^2=a^2-2ab+b^2\), the middle term is negative.
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What is the correct answer to this question?
\(k^2-8k+16\)
Why is this the correct answer?
The area of a square is the square of its side. Thus, \((k-4)^2=k^2-2\cdot k\cdot4+4^2=k^2-8k+16\). In the area model, two rectangular parts of area \(4k\) are removed from the \(k^2\) region, and the corner square of area \(16\) is added. Option A has only \(-4k\) as the middle term, but it should be \(-8k\). Exam tip: in \((a-b)^2=a^2-2ab+b^2\), the middle term is negative.
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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