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

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

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 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 + 8

Answer: −4(5x − 2)

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

Answer: 4(x2−x+1)

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

Answer: 5a(4b + 3)

  1. Highest common factor: 5a
  2. 20ab + 15a = 5a(4b + 3)
  3. Check by expanding the brackets.
4.Factorise fully: −8x + 72

Answer: −8(x − 9)

  1. Highest common factor: −8
  2. −8x + 72 = −8(x − 9)
  3. Check by expanding the brackets.
5.Factorise fully: 16x2 + 24x − 28

Answer: 4(4x2+6x−7)

  1. Highest common factor: 4
  2. 16x2 + 24x − 28 = 4(4x2 + 6x − 7)
  3. Check by expanding the brackets.
6.Factorise fully: 10ab − 18a

Answer: 2a(5b − 9)

  1. Highest common factor: 2a
  2. 10ab − 18a = 2a(5b − 9)
  3. Check by expanding the brackets.
7.Factorise fully: −21x − 49

Answer: −7(3x + 7)

  1. Highest common factor: −7
  2. −21x − 49 = −7(3x + 7)
  3. Check by expanding the brackets.
8.Factorise fully: 10x2 + 5x + 25

Answer: 5(2x2+x+5)

  1. Highest common factor: 5
  2. 10x2 + 5x + 25 = 5(2x2 + x + 5)
  3. Check by expanding the brackets.
9.Factorise fully: 20ab + 35a

Answer: 5a(4b + 7)

  1. Highest common factor: 5a
  2. 20ab + 35a = 5a(4b + 7)
  3. Check by expanding the brackets.
10.Factorise fully: −20x − 32

Answer: −4(5x + 8)

  1. Highest common factor: −4
  2. −20x − 32 = −4(5x + 8)
  3. Check by expanding the brackets.
11.Factorise fully: 12x2 − 12x − 8

Answer: 4(3x2−3x−2)

  1. Highest common factor: 4
  2. 12x2 − 12x − 8 = 4(3x2 − 3x − 2)
  3. Check by expanding the brackets.
12.Factorise fully: 3ab − 27a

Answer: 3a(b − 9)

  1. Highest common factor: 3a
  2. 3ab − 27a = 3a(b − 9)
  3. Check by expanding the brackets.
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