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Class 8 Maths — Algebraic identities

Use (a + b)², (a - b)² and a² - b² to expand brackets and to multiply quickly.

Name: ________________________

  1. 1.Expand (a + b)².

    • a) 2a + 2b
    • b) a² + b²
    • c) a² - 2ab + b²
    • d) a² + 2ab + b²

  2. 2.Use a² - b² = (a + b)(a - b) to work out 105 × 95.

  3. 3.Factorise a² - b².

    • a) (a + b)(a - b)
    • b) (a + b)(a + b)
    • c) a(a - b)
    • d) (a - b)(a - b)

  4. 4.Match each product to its expansion.

    • (x + 1)²
    • (x - 1)²
    • (x + 2)(x - 2)
    • (x + 4)²
    • x² - 4
    • x² + 8x + 16
    • x² - 2x + 1
    • x² + 2x + 1

  5. 5.Expand (x - 5)².

    • a) x² - 10x - 25
    • b) x² - 25
    • c) x² + 10x + 25
    • d) x² - 10x + 25

  6. 6.Expand (a - b)².

    • a) a² + 2ab + b²
    • b) a² + b²
    • c) a² - 2ab + b²
    • d) a² - b²

  7. 7.Use (100 - 2)² to work out 98².

  8. 8.Use (50 + 1)² to work out 51².

Answer key — Class 8 Maths — Algebraic identities

  1. 1. d) a² + 2ab + b²
  2. 2. 9975
  3. 3. a) (a + b)(a - b)
  4. 4. (x + 1)² → x² + 2x + 1; (x - 1)² → x² - 2x + 1; (x + 2)(x - 2) → x² - 4; (x + 4)² → x² + 8x + 16
  5. 5. d) x² - 10x + 25
  6. 6. c) a² - 2ab + b²
  7. 7. 9604
  8. 8. 2601