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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 3 — Answers

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

1.Factorise fully: −20x + 36

Answer: −4(5x − 9)

  1. Highest common factor: −4
  2. −20x + 36 = −4(5x − 9)
  3. Check by expanding the brackets.
2.Factorise fully: 8x2 + 10x − 18

Answer: 2(4x2+5x−9)

  1. Highest common factor: 2
  2. 8x2 + 10x − 18 = 2(4x2 + 5x − 9)
  3. Check by expanding the brackets.
3.Factorise fully: 6ab − 24a

Answer: 6a(b − 4)

  1. Highest common factor: 6a
  2. 6ab − 24a = 6a(b − 4)
  3. Check by expanding the brackets.
4.Factorise fully: −9x − 54

Answer: −9(x + 6)

  1. Highest common factor: −9
  2. −9x − 54 = −9(x + 6)
  3. Check by expanding the brackets.
5.Factorise fully: 24x2 + 18x + 30

Answer: 6(4x2+3x+5)

  1. Highest common factor: 6
  2. 24x2 + 18x + 30 = 6(4x2 + 3x + 5)
  3. Check by expanding the brackets.
6.Factorise fully: 4ab + 32a

Answer: 4a(b + 8)

  1. Highest common factor: 4a
  2. 4ab + 32a = 4a(b + 8)
  3. Check by expanding the brackets.
7.Factorise fully: −54x − 9

Answer: −9(6x + 1)

  1. Highest common factor: −9
  2. −54x − 9 = −9(6x + 1)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 − 8x − 8

Answer: 2(3x2−4x−4)

  1. Highest common factor: 2
  2. 6x2 − 8x − 8 = 2(3x2 − 4x − 4)
  3. Check by expanding the brackets.
9.Factorise fully: 5ab − 10a

Answer: 5a(b − 2)

  1. Highest common factor: 5a
  2. 5ab − 10a = 5a(b − 2)
  3. Check by expanding the brackets.
10.Factorise fully: −28x + 35

Answer: −7(4x − 5)

  1. Highest common factor: −7
  2. −28x + 35 = −7(4x − 5)
  3. Check by expanding the brackets.
11.Factorise fully: 15x2 + 35x + 15

Answer: 5(3x2+7x+3)

  1. Highest common factor: 5
  2. 15x2 + 35x + 15 = 5(3x2 + 7x + 3)
  3. Check by expanding the brackets.
12.Factorise fully: 15ab + 40a

Answer: 5a(3b + 8)

  1. Highest common factor: 5a
  2. 15ab + 40a = 5a(3b + 8)
  3. Check by expanding the brackets.
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