What is the difference between the area models of squares (x+5) and (x+1)?
Answer and explanation
Correct answer: \(8x+24\)
The side lengths of the two squares are \(x+5\) and \(x+1\), so the difference of their areas is \((x+5)^2-(x+1)^2\). Applying the difference-of-squares identity gives \((x+5)^2-(x+1)^2=[(x+5)+(x+1)]\,[(x+5)-(x+1)]\). Thus, \((2x+6)\times4=8x+24\). Therefore, \(8x+24\) is correct. In \(4x+24\), the coefficient of the \(x\)-term is incorrectly calculated when multiplying \(2x+6\) by 4. Exam tip: for a difference of square areas, use \(A^2-B^2=(A+B)(A-B)\) directly.
Frequently asked questions
What is the correct answer to this question?
\(8x+24\)
Why is this the correct answer?
The side lengths of the two squares are \(x+5\) and \(x+1\), so the difference of their areas is \((x+5)^2-(x+1)^2\). Applying the difference-of-squares identity gives \((x+5)^2-(x+1)^2=[(x+5)+(x+1)]\,[(x+5)-(x+1)]\). Thus, \((2x+6)\times4=8x+24\). Therefore, \(8x+24\) is correct. In \(4x+24\), the coefficient of the \(x\)-term is incorrectly calculated when multiplying \(2x+6\) by 4. Exam tip: for a difference of square areas, use \(A^2-B^2=(A+B)(A-B)\) directly.
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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