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

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

1.Factorise fully: −4x − 20

Answer: −4(x + 5)

  1. Highest common factor: −4
  2. −4x − 20 = −4(x + 5)
  3. Check by expanding the brackets.
2.Factorise fully: 8x2 + 10x − 16

Answer: 2(4x2+5x−8)

  1. Highest common factor: 2
  2. 8x2 + 10x − 16 = 2(4x2 + 5x − 8)
  3. Check by expanding the brackets.
3.Factorise fully: 5ab + 20a

Answer: 5a(b + 4)

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

Answer: −2(x − 2)

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

Answer: 4(3x2−4x+1)

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

Answer: 5a(b − 4)

  1. Highest common factor: 5a
  2. 5ab − 20a = 5a(b − 4)
  3. Check by expanding the brackets.
7.Factorise fully: −40x − 8

Answer: −8(5x + 1)

  1. Highest common factor: −8
  2. −40x − 8 = −8(5x + 1)
  3. Check by expanding the brackets.
8.Factorise fully: 4x2 + 10x − 6

Answer: 2(2x2+5x−3)

  1. Highest common factor: 2
  2. 4x2 + 10x − 6 = 2(2x2 + 5x − 3)
  3. Check by expanding the brackets.
9.Factorise fully: 8ab − 12a

Answer: 4a(2b − 3)

  1. Highest common factor: 4a
  2. 8ab − 12a = 4a(2b − 3)
  3. Check by expanding the brackets.
10.Factorise fully: −21x − 7

Answer: −7(3x + 1)

  1. Highest common factor: −7
  2. −21x − 7 = −7(3x + 1)
  3. Check by expanding the brackets.
11.Factorise fully: 12x2 − 20x − 36

Answer: 4(3x2−5x−9)

  1. Highest common factor: 4
  2. 12x2 − 20x − 36 = 4(3x2 − 5x − 9)
  3. Check by expanding the brackets.
12.Factorise fully: 4ab − 4a

Answer: 4a(b − 1)

  1. Highest common factor: 4a
  2. 4ab − 4a = 4a(b − 1)
  3. Check by expanding the brackets.
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