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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.

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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — Answers

Take out the highest common factor. Where the first term is negative, take out a negative factor.

1.Factorise fully: −27x − 18

Answer: −9(3x + 2)

  1. Highest common factor: −9
  2. −27x − 18 = −9(3x + 2)
  3. Check by expanding the brackets.
2.Factorise fully: 20x2 − 30x + 15

Answer: 5(4x2−6x+3)

  1. Highest common factor: 5
  2. 20x2 − 30x + 15 = 5(4x2 − 6x + 3)
  3. Check by expanding the brackets.
3.Factorise fully: 5ab − 25a

Answer: 5a(b − 5)

  1. Highest common factor: 5a
  2. 5ab − 25a = 5a(b − 5)
  3. Check by expanding the brackets.
4.Factorise fully: −16x − 56

Answer: −8(2x + 7)

  1. Highest common factor: −8
  2. −16x − 56 = −8(2x + 7)
  3. Check by expanding the brackets.
5.Factorise fully: 12x2 + 20x − 16

Answer: 4(3x2+5x−4)

  1. Highest common factor: 4
  2. 12x2 + 20x − 16 = 4(3x2 + 5x − 4)
  3. Check by expanding the brackets.
6.Factorise fully: 6ab + 27a

Answer: 3a(2b + 9)

  1. Highest common factor: 3a
  2. 6ab + 27a = 3a(2b + 9)
  3. Check by expanding the brackets.
7.Factorise fully: −9x + 15

Answer: −3(3x − 5)

  1. Highest common factor: −3
  2. −9x + 15 = −3(3x − 5)
  3. Check by expanding the brackets.
8.Factorise fully: 12x2 − 24x + 32

Answer: 4(3x2−6x+8)

  1. Highest common factor: 4
  2. 12x2 − 24x + 32 = 4(3x2 − 6x + 8)
  3. Check by expanding the brackets.
9.Factorise fully: 36ab − 6a

Answer: 6a(6b − 1)

  1. Highest common factor: 6a
  2. 36ab − 6a = 6a(6b − 1)
  3. Check by expanding the brackets.
10.Factorise fully: −8x + 20

Answer: −4(2x − 5)

  1. Highest common factor: −4
  2. −8x + 20 = −4(2x − 5)
  3. Check by expanding the brackets.
11.Factorise fully: 5x2 − 10x − 20

Answer: 5(x2−2x−4)

  1. Highest common factor: 5
  2. 5x2 − 10x − 20 = 5(x2 − 2x − 4)
  3. Check by expanding the brackets.
12.Factorise fully: 15ab − 21a

Answer: 3a(5b − 7)

  1. Highest common factor: 3a
  2. 15ab − 21a = 3a(5b − 7)
  3. Check by expanding the brackets.
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