Expanding brackets
Maths, Algebra. Usually met in years 8 to 10.
Multiply out brackets in algebra, from a single bracket to the product of two brackets.
What you practise
- Expanding a single bracket
- Expanding and simplifying two brackets
- Handling negative signs
Builds from k(x + a) to brackets like (2x + 3)(x − 5). Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Expand 4(3x + 5).
- 12x − 20
- 12x + 20
- 12x + 5
- 3x + 20
- 7x + 9
Show the answer and method
Answer: B, 12x + 20
The method: Multiply each term by 4: 12x and 20. So 12x + 20.
Why the other options are wrong:
- A, 12x − 20: The sign of the second term changed.
- C, 12x + 5: The number in the bracket was not multiplied by 4.
- D, 3x + 20: The 3x was not multiplied by 4.
- E, 7x + 9: The terms were added to the number outside instead of multiplied.
Sample question, level 4 of 5
Expand and simplify (x + 7)(x − 5).
- x² − 2x − 35
- x² + 2x − 35
- x² − 35
- x² + 2x + 35
- x² + 12x − 35
Show the answer and method
Answer: B, x² + 2x − 35
The method: Expand: x² − 5x + 7x − 35. Collect the x terms: 7 − 5 = 2. So x² + 2x − 35.
Why the other options are wrong:
- A, x² − 2x − 35: The x terms were subtracted the wrong way round.
- C, x² − 35: The x terms from the middle were left out.
- D, x² + 2x + 35: The last term is a positive times a negative, so it is negative.
- E, x² + 12x − 35: The x terms were added, but one is negative: +ax and −bx.
See where this fits: GCSE maths with AQA and Key Stage 3.
Related topics: Solving equations, Factorising quadratics, Sequences.
