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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesEasy
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A student took only one 3x strip in the model of (x+3)². What is the mistake?

Answer and explanation

Correct answer: He should take two 3x strips

The correct answer is A: he should take two 3x strips. Expand the square identity: (x+3)²=x²+2×x×3+3²=x²+6x+9. The visual model has one x² square, two rectangular strips of dimensions x by 3, and one 3 by 3 corner square. Each strip has area 3x, so together they contribute 6x. Taking only one strip gives x²+3x+9, which is incomplete and does not equal the square’s area. Option B is wrong because the middle contribution is 6x, not 9x. Options C and D remove parts that are required. Memory cue: squaring a binomial creates two cross-products, not one.

Related tags

Common-ErrorBinomial-SquareVisual-ModelVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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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 × b is removed. The remaining area is related to which expression?
  5. 5In a visual model, a²−b² 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 large \(a\times a\) 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 eight \(x\)-tiles. If there are 16 constant tiles, what complete square does the model represent?
  10. 10If, in a square model, the total area of the two middle rectangles is \(10x\) and the small square has area 25, what is the side of the complete square?
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