Grade 10 Maths · Algebra

Multiply out a single bracket

Multiply every term inside a bracket by the term outside it, watching the signs (for example −2x(x − 3) = −2x² + 6x).

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Gr 9 Products : Monomial on outsideKevinmathscience

Expanding & Simplifying Single Brackets - Tutorial / RevisionMe vs Maths

GCSE Maths - How to Expand Single Brackets (2026/27 exams)Cognito

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Question 1.3 · March 2022 · Provincial · 2 marks

Four options are provided as possible answers to the following questions. Choose the correct option.

1.3 Simplify the following:

- 3 x^{2} y (5 x y^{2} + x y) =

(2)

A $- 15 x^{2} y^{2} - 3 x^{2} y$
B $- 15 x^{3} y^{3} - 3 x^{3} y$
C $- 15 x^{3} y^{3} - 3 x^{3} y^{2}$
D $- 15 x^{3} y^{3} + x y$

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

More past paper questions: multiply out a single bracket

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3. Question 8.2.2 · May/June 2025 · Paper 1 · National (DBE) · 4 marks
8.2 Determine:
8.2.2 $g^{'} (x)$ if $g (x) = - 2 x (x - 1)^{2}$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Express the surd as an exponent $g (x) = - 2 x^{\frac{1}{2}} (x - 1)^{2}$
  1 mark · Write a root as a power
2. ✓
  Expand the squared binomial $g (x) = - 2 x^{\frac{1}{2}} (x^{2} - 2 x + 1)$
  1 mark · Square a binomial
3. ✓
  Multiply out the terms $g (x) = - 2 x^{\frac{5}{2}} + 4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}}$
  1 mark · Multiply out a single bracket
4. ✓
  Find the derivative term by term $g^{'} (x) = - 2 (\frac{5}{2}) x^{\frac{3}{2}} + 4 (\frac{3}{2}) x^{\frac{1}{2}} - 2 (\frac{1}{2}) x^{- \frac{1}{2}}$
  $g^{'} (x) = - 5 x^{\frac{3}{2}} + 6 x^{\frac{1}{2}} - x^{- \frac{1}{2}}$
  1 mark · Differentiate using the power rule
4. Question 1.5.1 · March 2022 · Provincial · 2 marks
1.5 Simplify completely:
1.5.1 $3 x (2 x - 4 x y)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  First term $3 x \cdot 2 x = 6 x^{2}$
  1 mark · Multiply out a single bracket
2. ✓
  Second term $3 x \cdot (- 4 x y) = - 12 x^{2} y$
  $= 6 x^{2} - 12 x^{2} y$
  1 mark · Multiply out a single bracket
5. Question 1.1.1 · March 2021 · Provincial · 2 marks
1.1 Determine the product of the following and simplify fully:
1.1.1 $a b^{2} (- 2 a^{2} + 4 b)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  First term $a b^{2} \cdot (- 2 a^{2}) = - 2 a^{3} b^{2}$
  1 mark · Multiply out a single bracket
2. ✓
  Second term $a b^{2} \cdot 4 b = 4 a b^{3}$ , so the product is $- 2 a^{3} b^{2} + 4 a b^{3}$
  1 mark · Multiply out a single bracket
6. Question 1.1.1 · September 2024 · Paper 1 · Provincial · 2 marks
1.1 Given: $2 k = (x - 5) (x - k)$ , determine:
1.1.1 $k$ if $x = 2$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Simplification $2 k = (2 - 5) (2 - k)$ $2 k = - 6 + 3 k$
  1 mark · Multiply out a single bracket
2. ✓
  Answer $k = 6$
  1 mark · Solve a linear equation

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