If a model of a square with side (g-1) is made, what will be the total area?
Answer and explanation
Correct answer: \(g^2-2g+1\)
The area of a square equals the square of its side. Therefore, for side \((g-1)\), the area is \((g-1)^2\). Applying \((a-b)^2=a^2-2ab+b^2\) with \(a=g\) and \(b=1\) gives \(g^2-2g+1\). The expression \(g^2-1\) is a difference of squares, not the square of a difference. Exam tip: the middle term in \((a-b)^2\) is always \(-2ab\).
Frequently asked questions
What is the correct answer to this question?
\(g^2-2g+1\)
Why is this the correct answer?
The area of a square equals the square of its side. Therefore, for side \((g-1)\), the area is \((g-1)^2\). Applying \((a-b)^2=a^2-2ab+b^2\) with \(a=g\) and \(b=1\) gives \(g^2-2g+1\). The expression \(g^2-1\) is a difference of squares, not the square of a difference. Exam tip: the middle term in \((a-b)^2\) 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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