Grade 10 Maths · Algebra

Square a binomial

Square a bracket with two terms, remembering the middle term (for example (x + 3)² = x² + 6x + 9, not x² + 9).

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Question 2.1 · March 2021 · Paper 1 · Provincial · 3 marks

2.1 Without using a calculator, rationalise the denominator and simplify:

\frac{3 - 2}{3 + 2}

(3)

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

More past paper questions: square a binomial

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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 2.1.3 · June 2025 · Paper 1 · Provincial · 3 marks
2.1 Simplify the following expressions fully:
2.1.3 $(4 x + 1)^{2} - (3 x + 1) (3 x - 1)$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Expand the square and the difference of two squares $= (16 x^{2} + 8 x + 1) - (9 x^{2} - 1)$
  2 marks · Square a binomial
2. ✓
  Simplify by combining like terms $= 16 x^{2} + 8 x + 1 - 9 x^{2} + 1$
  $= 7 x^{2} + 8 x + 2$
  1 mark · Collect like terms
5. Question 1.3.2 · March 2025 · Provincial · 2 marks
1.3 Simplify the following fully:
1.3.2 $(5 - 4 x)^{2}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Expand brackets $(5 - 4 x) (5 - 4 x) = 25 - 20 x - 20 x + 16 x^{2}$
  1 mark · Square a binomial
2. ✓
  Simplify $25 - 40 x + 16 x^{2}$
  1 mark · Collect like terms
6. Question 2.1.1 · June 2024 · Paper 1 · Provincial · 2 marks
2.1 Simplify the following:
2.1.1 $2 b (b - 5 c)^{2}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Square the binomial $= 2 b (b^{2} - 10 b c + 25 c^{2})$
  1 mark · Square a binomial
2. ✓
  Distribute 2b $= 2 b^{3} - 20 b^{2} c + 50 b c^{2}$
  1 mark · Multiply out a single bracket

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