Grade 10 Maths · Algebra

Multiply two binomials

Multiply two brackets by multiplying each term in the first by each term in the second (for example (x + 2)(x + 3) = x² + 5x + 6).

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Gr 9 Products : BinomialsKevinmathscience

1) Binomial x binomial | products grade 10Kevinmathscience

Multiplying Binomials by the FOIL MethodProfessor Dave Explains

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Question 1.3 · May/June 2024 · Paper 1 · National (DBE) · 3 marks

1.3 Given:

P = (1 - a)

and

T = (1 + a) (1 + a^{2}) (1 + a^{4}) ... (1 + a^{512})

. Determine the value of

P \times T

in terms of

a

.(3)

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

More past paper questions: multiply two binomials

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3. Question 1.2.3 · March 2023 · Provincial · 2 marks
If $x = 2$ and $y = - 2$ , decide whether the following expressions are rational, irrational or non-real:
1.2 Expand the following expressions:
1.2.3 $(\frac{a}{2} + 1) (\frac{a}{2} - 1)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  $\frac{a ^{2}}{4}$ $(\frac{a}{2} + 1) (\frac{a}{2} - 1) = \frac{a ^{2}}{4} \dots$
  1 mark · Multiply two binomials
2. ✓
  $- 1$ $= \frac{a ^{2}}{4} - 1$
  1 mark · Multiply two binomials
4. Question 1.1.2 · March 2018 · Provincial · 2 marks
1.1 Determine the product of the following expressions:
1.1.2 $(a + \frac{5}{a ^{x}}) (a - \frac{5}{a ^{x}})$ (2)
Show the memo (1 tick)Memo
1. ✓
  Apply difference of two squares $a^{2} - (\frac{5}{a ^{x}})^{2}$
  $= a^{2} - \frac{5}{a ^{2 x}}$
  2 marks · Multiply two binomials
5. Question 4.1.4 · June 2025 · Paper 1 · Provincial · 2 marks
4.1 Given: $f (x) = - x^{2} + 4$
4.1.4 Describe the transformation from $f$ to $h$ in words if $h (x) = - (x - 1) (x + 1)$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Expand the equation for h(x) $h (x) = - (x^{2} - 1)$
  $h (x) = - x^{2} + 1$
  1 mark · Multiply two binomials
2. ✓
  Describe the shiftThe graph of $f$ is shifted vertically down by $3$ units.
  1 mark · Shift a graph
6. Question 1.2.1 · March 2019 · Provincial · 3 marks
Factorise the following expressions fully:
1.2 Simplify the following expressions fully:
1.2.1 $(2 x + 3) (5 - x)$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Expand brackets $10 x - 2 x^{2} + 15 - 3 x$
  2 marks · Multiply two binomials
2. ✓
  Simplify $- 2 x^{2} + 7 x + 15$
  1 mark · Collect like terms

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