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ICSE Class 9 Algebra: expansions — practice questions

Explore 28 free Algebra: expansions questions in ICSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: expansions questions and exercises with answers

Showing questions 1–28 of 28.

Expanding (x + 3)(x + 5) gives which polynomial expression?Read the answer and worked solution →Multiply the two binomial factors (x + 6) and (x - 2).Read the answer and worked solution →Compute the algebraic product of (x - 3) with (x - 7).Read the answer and worked solution →Which formula represents the square of the sum (a + b)?Read the answer and worked solution →Determine the polynomial result when (2x - 3) is squared.Read the answer and worked solution →Expand the algebraic expression (3x + 2y)^2.Read the answer and worked solution →Given that a + b = 7 and ab = 10, evaluate a^2 + b^2.Read the answer and worked solution →Cutting a square of side a + b gives two squares and how many rectangles?Read the answer and worked solution →Simplify the difference of squares product (2x + 5)(2x - 5).Read the answer and worked solution →Calculate 103 × 97 quickly using an algebraic identity.Read the answer and worked solution →Which algebraic expression is identically equal to (a - b)^2?Read the answer and worked solution →Find the numerical value of (a - b)^2 when a + b = 9 and ab = 14.Read the answer and worked solution →Write down the expanded sum for the reciprocal square (x + 1/x)^2.Read the answer and worked solution →How does the squared difference with a reciprocal (x - 1/x)^2 expand?Read the answer and worked solution →Suppose x + 1/x = 5. Determine the value of x^2 + 1/x^2.Read the answer and worked solution →For a variable x satisfying x - 1/x = 4, evaluate x^2 + 1/x^2.Read the answer and worked solution →When x + 1/x equals 3, compute the fourth power sum x^4 + 1/x^4.Read the answer and worked solution →Expand the trinomial (a + b + c)^2.Read the answer and worked solution →What does (x + y - z)^2 expand to?Read the answer and worked solution →If a + b + c = 9 and ab + bc + ca = 23, find a^2 + b^2 + c^2.Read the answer and worked solution →According to the binomial theorem, what does (x + y)^3 expand to?Read the answer and worked solution →Cubing the binomial (x + 2) yields which polynomial?Read the answer and worked solution →Find the simplified expression for the cube of (x - 2).Read the answer and worked solution →How many rectangular boxes are formed when a cube of side a + b is cut?Read the answer and worked solution →Match each three-variable identity with its expanded polynomial:Read the answer and worked solution →Match each cubic identity with its algebraic expansion:Read the answer and worked solution →Match each special conditional cubic identity with its result:Read the answer and worked solution →Match each binomial product with its expansion:Read the answer and worked solution →

Worked practice questions

Expanding (x + 3)(x + 5) gives which polynomial expression?

  1. x^2 + 8x + 15
  2. x^2 + 15x + 8
  3. x^2 + 8x + 8
  4. x^2 + 15x + 15
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Correct answer: A. x^2 + 8x + 15

Applying the distributive law yields x^2 + 5x + 3x + 15 which simplifies to x^2 + 8x + 15.

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Multiply the two binomial factors (x + 6) and (x - 2).

  1. x^2 - 4x - 12
  2. x^2 + 4x - 12
  3. x^2 + 8x - 12
  4. x^2 + 4x + 12
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Correct answer: B. x^2 + 4x - 12

Multiplying each term gives x^2 - 2x + 6x - 12, which simplifies to x^2 + 4x - 12.

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Compute the algebraic product of (x - 3) with (x - 7).

  1. x^2 + 10x + 21
  2. x^2 - 10x - 21
  3. x^2 - 10x + 21
  4. x^2 - 21x + 10
Show answer and solution

Correct answer: C. x^2 - 10x + 21

Distributing terms gives x^2 - 7x - 3x + 21, which equals x^2 - 10x + 21.

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More Mathematics topics

Coordinate GeometryAlgebra: factorisationAlgebra: logarithmsGeometry: Pythagoras theoremGeometry: triangles (congruency, mid-point theorem)MensurationPythagoras TheoremAlgebra: indices