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Year 9 Mathematics · Expanding and factorising expressions

Name: ______________________

Date: ____________

  1. 1. Expand 5(x + 2).

    • ☐ (a) 5x + 2
    • ☐ (b) 5x + 10
    • ☐ (c) x + 10
    • ☐ (d) 5x + 7

  2. 2. Expand −3(y − 4).

    • ☐ (a) −3y − 12
    • ☐ (b) −3y + 12
    • ☐ (c) 3y − 12
    • ☐ (d) −3y − 4

  3. 3. What is the highest common factor of 12x and 18?

    • ☐ (a) 6
    • ☐ (b) 6x
    • ☐ (c) 3
    • ☐ (d) 12

  4. 4. Factorise 10m − 15 fully.

    • ☐ (a) 5(2m − 3)
    • ☐ (b) 10(m − 15)
    • ☐ (c) 5(2m − 15)
    • ☐ (d) 5(m − 3)

  5. 5. Expand 4(2a + 3).

  6. 6. Expand and simplify 2(x + 5) + 3(x − 1).

  7. 7. Factorise 7x + 21.

  8. 8. Factorise 6p² + 9p fully.

Answer sheet

  1. 1. 5x + 10 — Multiply both terms by 5: 5 × x = 5x and 5 × 2 = 10.
  2. 2. −3y + 12 — −3 × y = −3y and −3 × −4 = +12.
  3. 3. 6 — The HCF of 12 and 18 is 6. The term 18 has no x, so x is not a common factor.
  4. 4. 5(2m − 3) — The HCF is 5: 10m ÷ 5 = 2m and 15 ÷ 5 = 3, giving 5(2m − 3). Check: 5 × 2m − 5 × 3 = 10m − 15.
  5. 5. 8a + 12 — 4 × 2a = 8a and 4 × 3 = 12.
  6. 6. 5x + 7 — 2x + 10 + 3x − 3. Collect like terms: 5x + 7.
  7. 7. 7(x + 3) — The HCF of 7x and 21 is 7. 7x ÷ 7 = x and 21 ÷ 7 = 3.
  8. 8. 3p(2p + 3) — The HCF of 6p² and 9p is 3p. 6p² ÷ 3p = 2p and 9p ÷ 3p = 3. Check: 3p × 2p + 3p × 3 = 6p² + 9p.

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