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Which algebraic expression is best represented by an area model that divides a large square into four parts—two squares of different sizes and two congruent rectangles?
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Answer and explanation
Correct answer: \(a^2+2ab+b^2\)
Splitting a square of side \(a+b\) gives areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Their sum is \(a^2+2ab+b^2\). \(a^2-b^2\) represents a difference, not this complete square model. Exam tip: count both \(ab\) rectangles.
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What is the correct answer to this question?
\(a^2+2ab+b^2\)
Why is this the correct answer?
Splitting a square of side \(a+b\) gives areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Their sum is \(a^2+2ab+b^2\). \(a^2-b^2\) represents a difference, not this complete square model. Exam tip: count both \(ab\) rectangles.
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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