7 · Brackets (Distributive)
Expand and factorise brackets, and solve equations that contain them.
What your child learns
- a(b + c) = ab + ac
- Factorise by taking out the biggest common factor
- Solve equations with brackets
Example
3(x + 4) = 3x + 12; 6x + 9 = 3(2x + 3).
Mini lesson: Brackets & the Distributive Property
Goal: Expand brackets, factorise, and solve equations with brackets.
The number outside a bracket multiplies everything inside: a(b + c) = ab + ac.
- 3(x + 4) = 3x + 12
- −2(x − 5) = −2x + 10 (negative × negative = positive)
- Factorising is the reverse: 6x + 9 = 3(2x + 3).
Worked example
Solve 4(x + 2) = 28.
- Expand: 4x + 8 = 28
- Subtract 8: 4x = 20
- Divide by 4: x = 5
Common mistakes
- Multiplying only the first term: 3(x + 4) → 3x + 4.
- Sign errors with negatives outside the bracket.
Practice questions
A taste of the questions in BloomTracks – the app makes fresh ones every time and adjusts the level as your child answers.
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Question 1 · Level 1
Expand 7(x + 6)
Show the answer
Answer: 7x+42
7x + 42
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Question 2 · Level 3
Solve: 2(x + 4) = 16
Show the answer
Answer: 4
x + 4 = 8, so x = 4.
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Question 3 · Level 5
Expand and simplify 9(x + 6) − 5(x − 6)
Show the answer
Answer: 4x+84
4x + 84
Try it at home
Use money: 3 bags each with $2 and 5¢ → 3 × $2 + 3 × 5¢.
Key takeaway
Multiply EVERY term inside the bracket.
Practise 7 · brackets (distributive) with Bloomie
Bloomie reads every question aloud, listens to spoken answers and adapts the difficulty one question at a time.