What is the difference between the areas of squares with sides (x-1) and (x+1)?
Answer and explanation
Correct answer: \(4x\)
The larger square has area \((x+1)^2\), and the smaller square has area \((x-1)^2\). Thus, the difference in their areas is \((x+1)^2-(x-1)^2\). On expanding, \((x^2+2x+1)-(x^2-2x+1)=4x\). The expression \(x^2-1\) is the product \((x-1)(x+1)\), not the difference of the two square areas. Exam tip: write the larger area first and subtract the smaller area.
Frequently asked questions
What is the correct answer to this question?
\(4x\)
Why is this the correct answer?
The larger square has area \((x+1)^2\), and the smaller square has area \((x-1)^2\). Thus, the difference in their areas is \((x+1)^2-(x-1)^2\). On expanding, \((x^2+2x+1)-(x^2-2x+1)=4x\). The expression \(x^2-1\) is the product \((x-1)(x+1)\), not the difference of the two square areas. Exam tip: write the larger area first and subtract the smaller area.
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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