Grade 10 Maths · Algebra

Factorise by grouping in pairs

Factorise four terms by grouping them in pairs and taking out the common bracket (for example ax + ay + bx + by = (a + b)(x + y)).

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9) Grouping Factorisation grade 10Kevinmathscience

Factorising using Grouping Grade 10 Maths Explanation and examplesMiss Martins Maths and Science

Gr 9 Factorisation: Grouping IntroductionKevinmathscience

Factoring | Grouping (Grade 10)Dr Gatsis Explains Math

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Question 2.2 · June 2024 · Paper 1 · Provincial · 3 marks

2.2 Factorise completely:

a^{2} - a x - 1 + x

(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: factorise by grouping in pairs

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3. Question 1.3.4 · March 2025 · Provincial · 3 marks
1.3 Factorise the following expressions fully.
1.3.4 $3 x - 6 x y - 2 y + 1$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Group terms $3 x (1 - 2 y) + 1 (- 2 y + 1)$
  2 marks · Factorise by grouping in pairs
2. ✓
  Extract common bracket $(3 x + 1) (1 - 2 y)$
  1 mark · Factorise by grouping in pairs
4. Question 1.4.2 · March 2024 · Provincial · 3 marks
1.4 Factorise the following expressions fully:
1.4.2 $2 x^{3} + x^{2} - 6 x - 3$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Group terms and factor out $x^{2} (2 x + 1) - 3 (2 x + 1)$
  1 mark · Factorise by grouping in pairs
2. ✓
  Final factors $(x^{2} - 3) (2 x + 1)$
  2 marks · Factorise by grouping in pairs
5. Question 1.3.2 · March 2023 · Provincial · 3 marks
If $x \in {- 2; 2; 4; 5}$ , choose the value of $x$ from the given set that will make the expression $\frac{18}{4 - x}$ be:
1.3 Factorise the following expressions fully:
1.3.2 $6 z^{2} y - 10 zy + 15 z - 25$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Common factor of first pair $6 z^{2} y - 10 zy = 2 zy (3 z - 5)$
  1 mark · Factorise by grouping in pairs
2. ✓
  Common factor of second pair $15 z - 25 = 5 (3 z - 5)$
  1 mark · Factorise by grouping in pairs
3. ✓
  Common bracket $(2 zy + 5) (3 z - 5)$
  1 mark · Factorise by grouping in pairs
6. Question 1.4.3 · March 2023 · Provincial · 3 marks
If $x = 2$ and $y = - 2$ , decide whether the following expressions are rational, irrational or non-real:
1.4 Factorise the following:
1.4.3 $a^{2} - 2 ab - 2 b^{2} + ab$ (3)
Show the memo (3 ticks)Memo
1. ✓
  $a (a - 2 b)$ $a^{2} - 2 ab - 2 b^{2} + ab = a (a - 2 b) \dots$
  1 mark · Factorise by grouping in pairs
2. ✓
  $b (a - 2 b)$ $= a (a - 2 b) + b (a - 2 b)$
  1 mark · Factorise by grouping in pairs
3. ✓
  Answer $= (a + b) (a - 2 b)$
  1 mark · Factorise by grouping in pairs

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