Expanding brackets

Algebra

Questions marked Higher are aimed at the Higher tier.

These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.

Expand $3(x + 4)$.

2 marks
Expand $4(2x - 5)$.

2 marks
Expand and simplify $2(x + 3) + 5(x - 1)$.

3 marks
Expand $(x + 4)(x + 3)$.

3 marks
Expand $(2x - 1)(x + 5)$.

4 marks
Expand and simplify $(x + 3)^{2} - (x - 2)^{2}$.

4 marks
Expand and simplify $(x + 2)(x - 3)(x + 1)$. Higher

5 marks
Expand and simplify $(2x + 1)^{3}$. Higher

6 marks

Mark scheme

Answer. $3x + 12$
- $3 \times x$ and $3 \times 4$
- $3x + 12$
Answer. $8x - 20$
- $4 \times 2x = 8x$ and $4 \times (-5) = -20$.
- $8x - 20$
Answer. $7x + 1$
- $2x + 6 + 5x - 5$
- $7x + 1$
Answer. $x^{2} + 7x + 12$
- $x^{2} + 3x + 4x + 12$
- $x^{2} + 7x + 12$
Answer. $2x^{2} + 9x - 5$
- $2x^{2} + 10x - x - 5$
- $2x^{2} + 9x - 5$
Answer. $10x + 5$
- $x^{2} + 6x + 9 - (x^{2} - 4x + 4)$
- $10x + 5$
Answer. $x^{3} - 7x - 6$
- $(x + 2)(x - 3) = x^{2} - x - 6$
- $(x^{2} - x - 6)(x + 1) = x^{3} + x^{2} - x^{2} - x - 6x - 6$
- $x^{3} - 7x - 6$
Answer. $8x^{3} + 12x^{2} + 6x + 1$
- $(2x + 1)^{2} = 4x^{2} + 4x + 1$
- $(4x^{2} + 4x + 1)(2x + 1) = 8x^{3} + 4x^{2} + 8x^{2} + 4x + 2x + 1$
- $8x^{3} + 12x^{2} + 6x + 1$