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Grade 9 Math — 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) a² + 2ab + b²
    • b) 2a + 2b
    • c) a² + b²
    • d) a² - 2ab + b²

  2. 2.Match each product to its expansion.

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

  3. 3.Expand (x + 3)².

    • a) x² + 9
    • b) x² + 6x + 6
    • c) x² + 6x + 9
    • d) x² + 3x + 9

  4. 4.Use (100 + 2)² to work out 102².

  5. 5.Use a² - b² = (a + b)(a - b) to work out 43² - 37².

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

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

  8. 8.Expand (a - b)².

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

Answer key — Grade 9 Math — Algebraic identities

  1. 1. a) a² + 2ab + b²
  2. 2. (x + 1)² → x² + 2x + 1; (x - 1)² → x² - 2x + 1; (x + 2)(x - 2) → x² - 4; (x + 4)² → x² + 8x + 16
  3. 3. c) x² + 6x + 9
  4. 4. 10404
  5. 5. 480
  6. 6. 9604
  7. 7. 9975
  8. 8. d) a² - 2ab + b²