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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesMediumLevel 69
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In the area model of a square with side a+b a+b , which shapes represent the term 2ab ?

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Answer and explanation

Correct answer: Two rectangles, each with sides \(a\) and \(b\)

In the area model of \((a+b)^2\), there is one \(a^2\) square, one \(b^2\) square, and two \(a\times b\) rectangles. Their areas add as \(ab+ab=2ab\). Exam tip: identify each region by multiplying its side lengths.

Related tags

Algebraic IdentitiesVisual ModelsArea ModelSquare ExpansionClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

Two rectangles, each with sides \(a\) and \(b\)

Why is this the correct answer?

In the area model of \((a+b)^2\), there is one \(a^2\) square, one \(b^2\) square, and two \(a\times b\) rectangles. Their areas add as \(ab+ab=2ab\). Exam tip: identify each region by multiplying its side lengths.

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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10 more MCQs
  1. 1A square has side \(a+b\). Which identity is shown by its area model?
  2. 2A diagram has two small squares with sides \(a\) and \(b\) and two equal rectangles. What is the total area?
  3. 3If the side of a big square is \(x+3\), how will its area be written?
  4. 4A square has side \(a\). A corner square of \(b \times b\) is removed. The remaining area is related to which expression?
  5. 5In a visual model \(a^2-b^2\) is rearranged into two rectangles. Which factorisation does it show?
  6. 6What is the area of a square with side \(a-b\)?
  7. 7In a diagram two \(a \times b\) rectangles are subtracted from a big \(a \times a\) square and a \(b \times b\) square is added back. Which identity is formed?
  8. 8What is the area of a rectangle with length \(x+2\) and breadth \(x+5\) in visual form?
  9. 9In a tile model there is one \(x^2\) tile and \(8\) \(x\)-tiles. If there are \(16\) constant tiles then the complete square models what?
  10. 10If in a square model the total area of the two middle rectangles is \(10x\) and the small square area is \(25\), what is the side?
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