← Back to the activity

Year 8 Maths — Factorisation

Break an algebraic expression into factors, and use those factors to divide one expression by another.

Name: ________________________

  1. 1.Which of these is x² + 10x + 25 written in factorised form?

    • a) (x + 5)²
    • b) (x + 10)²
    • c) (x + 25)(x + 1)
    • d) (x + 5)(x - 5)

  2. 2.Divide x² + 5x + 6 by x + 2. Write the answer.

  3. 3.Take a out of a² + ab as a common factor. What is left inside the bracket?

  4. 4.Put these expressions in order by the highest common factor of their terms, smallest first.

    • 14x + 21
    • 4x + 8
    • 10x + 25
    • 6x + 18
    • 3x + 9

  5. 5.Which of these is 4x² - 9 written in factorised form?

    • a) (2x - 3)(2x - 3)
    • b) (2x - 9)(2x + 1)
    • c) (2x - 3)(2x + 3)
    • d) (4x - 3)(x + 3)

  6. 6.Take 5 out of 5y - 20 as a common factor. What is left inside the bracket?

  7. 7.Divide 24y³ - 16y² by 8y². Write the answer.

  8. 8.Match each expression to its factorised form.

    • x² - 16
    • x² + 8x + 16
    • 3x + 12
    • x² - 4x
    • 2x² - 32
    • 2(x - 4)(x + 4)
    • (x - 4)(x + 4)
    • x(x - 4)
    • (x + 4)²
    • 3(x + 4)

Answer key — Year 8 Maths — Factorisation

  1. 1. a) (x + 5)²
  2. 2. x + 3
  3. 3. a + b
  4. 4. 1. 3x + 9 2. 4x + 8 3. 10x + 25 4. 6x + 18 5. 14x + 21
  5. 5. c) (2x - 3)(2x + 3)
  6. 6. y - 4
  7. 7. 3y - 2
  8. 8. x² - 16 → (x - 4)(x + 4); x² + 8x + 16 → (x + 4)²; 3x + 12 → 3(x + 4); x² - 4x → x(x - 4); 2x² - 32 → 2(x - 4)(x + 4)