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Which algebraic identity is represented by a visual model that divides a large square into four parts with areas \(a^2\), \(ab\), \(ab\), and \(b^2\), respectively?
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Answer and explanation
Correct answer: \((a+b)^2=a^2+2ab+b^2\)
The large square has side \(a+b\), so its area is \((a+b)^2\). Adding the four regions gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Exam tip: identify both \(ab\) rectangles before choosing the identity.
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What is the correct answer to this question?
\((a+b)^2=a^2+2ab+b^2\)
Why is this the correct answer?
The large square has side \(a+b\), so its area is \((a+b)^2\). Adding the four regions gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Exam tip: identify both \(ab\) rectangles before choosing the identity.
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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