Grade 10 Maths · Algebra

Factorise a difference of squares

Factorise one square minus another square into two brackets (for example x² − 9 = (x − 3)(x + 3)).

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Gr 9 Factorisation: Difference of Squares IntroductionKevinmathscience

7) Difference of two squares | factorisation grade 10Kevinmathscience

Gr 9 Factorisation: Difference of Squares PracticeKevinmathscience

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Question 1.3 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

1.3 Show that

(1 + x^{m} + x^{- n})^{2} - (1 - x^{m} - x^{- n})^{2}

is divisible by

2

for all real values of

m

and

n

.(3)

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

More past paper questions: factorise a difference of squares

Work each one out first, then open the memo and check every tick.

3. Question 1.4.3 · March 2024 · Provincial · 3 marks
1.4 Factorise the following expressions fully:
1.4.3 $x^{4} - 16$ (3)
Show the memo (2 ticks)Memo
1. ✓
  First difference of squares $(x^{2} - 4) (x^{2} + 4)$
  1 mark · Factorise a difference of squares
2. ✓
  Second difference of squares $(x - 2) (x + 2) (x^{2} + 4)$
  2 marks · Factorise a difference of squares
4. Question 1.3.1 · March 2023 · Provincial · 2 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:
1.3.1 $x^{4} - 16$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Difference of squares first step $(x^{2} - 4) (x^{2} + 4)$
  1 mark · Factorise a difference of squares
2. ✓
  Difference of squares second step $(x - 2) (x + 2) (x^{2} + 4)$
  1 mark · Factorise a difference of squares
5. Question 1.4.1 · March 2025 · Provincial · 2 marks
1.4 Factorise the following expressions fully:
1.4.1 $2 x^{2} - 18$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Common factor $2 (x^{2} - 9)$
  1 mark · Take out a common factor
2. ✓
  Difference of squares $2 (x - 3) (x + 3)$
  1 mark · Factorise a difference of squares
6. Question 3.1.2 · June 2024 · Paper 1 · Provincial · 4 marks
3.1 Solve for x:
3.1.2 $\frac{7}{3 - x} = \frac{5}{x + 3} + \frac{4}{x ^{2} - 9}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise denominators and adjust signs $\frac{- 7}{x - 3} = \frac{5}{x + 3} + \frac{4}{( x - 3 ) ( x + 3 )}$
  2 marks · Factorise a difference of squares
2. ✓
  Multiply by LCD and solve linear equation $- 7 (x + 3) = 5 (x - 3) + 4$
  $- 7 x - 21 = 5 x - 15 + 4$
  $- 12 x = 10$
  1 mark · Clear fractions in an equation
3. ✓
  Final answer $x = - \frac{10}{12}$
  $x = - \frac{5}{6}$
  1 mark · Clear fractions in an equation

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