Free Grade 3 Expanding Double Brackets Quizzes
Free Grade 3 quizzes for Expanding Double Brackets: 12 real questions with a full answer key and worked solutions. An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
Free
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain expanding double brackets
Explain expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate expanding double brackets
Calculate expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare expanding double brackets
Compare expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify expanding double brackets
Justify expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Expanding Double Brackets works
An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the value of 2x + 16 when x = 4.[1]
- 2.Find the value of 3x + 4 when x = 9.[1]
- 3.Find the value of 8x + 16 when x = 4.[1]
- 4.Find the value of 2x + 6 when x = 3.[1]
- 5.Simplify 9x + 4y + 2x − 5y.[2]
- 6.Simplify 6x + 1y + 4x − 5y.[2]
- 7.Simplify 5x + 4y + 6x − 8y.[2]
- 8.Simplify 7x + 9y + 2x − 2y.[2]
- 9.Expand 4(3x + 7).[3]
- 10.Expand 4(4x + 9).[3]
- 11.Expand 4(5x + 8).[3]
- 12.Expand 4(4x + 8).[3]
Show answers and working
1. 24
Replace x with 4: 2 × 4 + 16. 8 + 16 = 24.
2. 31
Replace x with 9: 3 × 9 + 4. 27 + 4 = 31.
3. 48
Replace x with 4: 8 × 4 + 16. 32 + 16 = 48.
4. 12
Replace x with 3: 2 × 3 + 6. 6 + 6 = 12.
5. 11x − 1y
Collect x terms: 9x + 2x = 11x. Collect y terms: 4y − 5y = -1y.
6. 10x − 4y
Collect x terms: 6x + 4x = 10x. Collect y terms: 1y − 5y = -4y.
7. 11x − 4y
Collect x terms: 5x + 6x = 11x. Collect y terms: 4y − 8y = -4y.
8. 9x + 7y
Collect x terms: 7x + 2x = 9x. Collect y terms: 9y − 2y = 7y.
9. 12x + 28
Multiply each term inside by 4. 4 × 3x = 12x, 4 × 7 = 28.
10. 16x + 36
Multiply each term inside by 4. 4 × 4x = 16x, 4 × 9 = 36.
11. 20x + 32
Multiply each term inside by 4. 4 × 5x = 20x, 4 × 8 = 32.
12. 16x + 32
Multiply each term inside by 4. 4 × 4x = 16x, 4 × 8 = 32.
Worked examples
Find the value of 9x + 16 when x = 5.
- Replace x with 5: 9 × 5 + 16.
- 45 + 16 = 61.
- Answer: 61
Simplify 4x + 7y + 7x − 3y.
- Collect x terms: 4x + 7x = 11x.
- Collect y terms: 7y − 3y = 4y.
- Answer: 11x + 4y
Expand 5(5x + 7).
- Multiply each term inside by 5.
- 5 × 5x = 25x, 5 × 7 = 35.
- Answer: 25x + 35
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads 3x as 3 + x, or as 3 with x stuck on.
Correction: 3x means 3 × x.
Only multiplies the first term when expanding.
Correction: Draw arrows from the outside to every inside term.
Teacher tips
- · Use algebra tiles to show collecting like terms.
Parent tips
- · Ask what 'number of pizzas × price' is for different orders.
Real-life applications
- · Formulas for cost: total = 5n + 2 for n items plus delivery.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Expanding Double Brackets quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Sequences. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Expanding Double Brackets?
- Move on to Factorising Quadratics, Completing the Square, The Quadratic Formula, Quadratic Graphs, which build directly on this idea.
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