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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesMedium
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In which square model will 9x² + 30x + 25 appear?

Answer and explanation

Correct answer: A square with side 3x + 5

The correct answer is a square with side 3x + 5. Use the identity (a + b)² = a² + 2ab + b². In the given expression, 9x² is (3x)² and 25 is 5². The middle term predicted by the identity is 2(3x)(5) = 30x, which is exactly the given middle term. Therefore, 9x² + 30x + 25 = (3x + 5)², so a square whose side is 3x + 5 represents the expression. Option B is incorrect because squaring 9x + 25 would produce much higher-degree and different terms. Option C gives (3x − 5)² = 9x² − 30x + 25, with a negative middle term. Option D also gives the wrong expansion. Check the first and last terms by taking their square roots, then verify the middle term by doubling their product.

Related tags

Perfect SquareVisual SquareAlgebraic IdentityQuadratic ExpressionVisual 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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