If a square of side \(p+q\) is divided according to lengths \(p\) and \(q\), which parts must appear in the visual area model of \((p+q)^2\)?
Answer and explanation
Correct answer: One \(p^2\) square, one \(q^2\) square, and two \(pq\) rectangles
Dividing the square in both directions at \(p\) and \(q\) gives \(p\times p=p^2\), \(q\times q=q^2\), and two \(p\times q\) regions. Thus the area is \(p^2+2pq+q^2\). Exam tip: count both \(pq\) rectangles.
Frequently asked questions
What is the correct answer to this question?
One \(p^2\) square, one \(q^2\) square, and two \(pq\) rectangles
Why is this the correct answer?
Dividing the square in both directions at \(p\) and \(q\) gives \(p\times p=p^2\), \(q\times q=q^2\), and two \(p\times q\) regions. Thus the area is \(p^2+2pq+q^2\). Exam tip: count both \(pq\) 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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