Inside a square of side (x+4), a square of side (x-4) is drawn. What is the difference of the two areas?
Answer and explanation
Correct answer: \(16x\)
The area of the larger square is \((x+4)^2\), and that of the smaller square is \((x-4)^2\). Thus, the difference is \((x+4)^2-(x-4)^2\). Using \((a+b)^2-(a-b)^2=4ab\), with \(a=x\) and \(b=4\), we get \(4\times x\times4=16x\). The expression \(x^2-16\) is the area of the smaller square, not the difference of the areas. Exam tip: subtract the smaller area from the larger area before simplifying.
Frequently asked questions
What is the correct answer to this question?
\(16x\)
Why is this the correct answer?
The area of the larger square is \((x+4)^2\), and that of the smaller square is \((x-4)^2\). Thus, the difference is \((x+4)^2-(x-4)^2\). Using \((a+b)^2-(a-b)^2=4ab\), with \(a=x\) and \(b=4\), we get \(4\times x\times4=16x\). The expression \(x^2-16\) is the area of the smaller square, not the difference of the areas. Exam tip: subtract the smaller area from the larger area before simplifying.
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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