What is the difference between the areas of a square of side (x+1) and a square of side (x-1)?
Answer and explanation
Correct answer: \(4x\)
The areas of the squares are \((x+1)^2\) and \((x-1)^2\). Thus, their difference is \((x+1)^2-(x-1)^2\). Applying the identity for the difference of squares gives \([(x+1)-(x-1)]\,[(x+1)+(x-1)]=2\times 2x=4x\). The expression \(x^2-1\) is the product \((x+1)(x-1)\), not the difference between the areas. Exam tip: For an area difference, write the larger square's area first and then use \(a^2-b^2\).
Frequently asked questions
What is the correct answer to this question?
\(4x\)
Why is this the correct answer?
The areas of the squares are \((x+1)^2\) and \((x-1)^2\). Thus, their difference is \((x+1)^2-(x-1)^2\). Applying the identity for the difference of squares gives \([(x+1)-(x-1)]\,[(x+1)+(x-1)]=2\times 2x=4x\). The expression \(x^2-1\) is the product \((x+1)(x-1)\), not the difference between the areas. Exam tip: For an area difference, write the larger square's area first and then use \(a^2-b^2\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
