A rectangle is made with sides (x+5) and (x+5). If it is treated as a square model, which special fact is correct?
Answer and explanation
Correct answer: The middle term will be \(10x\)
Each side of the square is \(x+5\), so its area is \((x+5)^2=x^2+2\times x\times5+25=x^2+10x+25\). Hence, the two equal rectangular strips together give \(10x\), the middle term. The constant term is \(25\), not \(10\). Exam tip: in \((a+b)^2\), the middle term is always \(2ab\).
Frequently asked questions
What is the correct answer to this question?
The middle term will be \(10x\)
Why is this the correct answer?
Each side of the square is \(x+5\), so its area is \((x+5)^2=x^2+2\times x\times5+25=x^2+10x+25\). Hence, the two equal rectangular strips together give \(10x\), the middle term. The constant term is \(25\), not \(10\). Exam tip: in \((a+b)^2\), the middle term is always \(2ab\).
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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