← Back to the activity

Year 9 Maths — Algebraic identities

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

Name: ________________________

  1. 1.Factorise a² - b².

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

  2. 2.Expand (a - b)².

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

  3. 3.Use (50 + 1)² to work out 51².

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

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

  6. 6.Match each product to its expansion.

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

  7. 7.If a + b = 10 and ab = 21, what is a² + b²?

  8. 8.Expand (x + 3)².

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

Answer key — Year 9 Maths — Algebraic identities

  1. 1. a) (a + b)(a - b)
  2. 2. d) a² - 2ab + b²
  3. 3. 2601
  4. 4. 10404
  5. 5. 9604
  6. 6. (x + 1)² → x² + 2x + 1; (x - 1)² → x² - 2x + 1; (x + 2)(x - 2) → x² - 4; (x + 4)² → x² + 8x + 16
  7. 7. 58
  8. 8. c) x² + 6x + 9