Which area model represents the identity \((a+b)^2=a^2+2ab+b^2\)?
Answer and explanation
Correct answer: A square of side \(a+b\) divided into \(a^2\), \(b^2\), and two \(ab\) rectangles
A square with side \(a+b\) contains squares of areas \(a^2\) and \(b^2\), plus two rectangles of area \(ab\). Thus its area is \(a^2+2ab+b^2\). Option B represents \(a^2-b^2\). Exam tip: always count both \(ab\) regions.
Frequently asked questions
What is the correct answer to this question?
A square of side \(a+b\) divided into \(a^2\), \(b^2\), and two \(ab\) rectangles
Why is this the correct answer?
A square with side \(a+b\) contains squares of areas \(a^2\) and \(b^2\), plus two rectangles of area \(ab\). Thus its area is \(a^2+2ab+b^2\). Option B represents \(a^2-b^2\). Exam tip: always count both \(ab\) regions.
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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