Free Grade 3 Working with Expanding Double Brackets Flashcards
Free Grade 3 flashcards for Working with 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with expanding double brackets
Explain working with expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with expanding double brackets
Calculate working with expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with expanding double brackets
Compare working with expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with expanding double brackets
Justify working with 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 Working with 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 9x + 14 when x = 9.[1]
- 2.Find the value of 2x + 18 when x = 8.[1]
- 3.Find the value of 3x + 15 when x = 3.[1]
- 4.Find the value of 9x + 8 when x = 6.[1]
- 5.Simplify 4x + 3y + 2x − 2y.[2]
- 6.Simplify 3x + 6y + 6x − 8y.[2]
- 7.Simplify 8x + 5y + 8x − 3y.[2]
- 8.Simplify 5x + 6y + 5x − 1y.[2]
- 9.Expand 2(5x + 1).[3]
- 10.Expand 2(5x + 9).[3]
- 11.Expand 5(3x + 9).[3]
- 12.Expand 4(6x + 5).[3]
Show answers and working
1. 95
Replace x with 9: 9 × 9 + 14. 81 + 14 = 95.
2. 34
Replace x with 8: 2 × 8 + 18. 16 + 18 = 34.
3. 24
Replace x with 3: 3 × 3 + 15. 9 + 15 = 24.
4. 62
Replace x with 6: 9 × 6 + 8. 54 + 8 = 62.
5. 6x + 1y
Collect x terms: 4x + 2x = 6x. Collect y terms: 3y − 2y = 1y.
6. 9x − 2y
Collect x terms: 3x + 6x = 9x. Collect y terms: 6y − 8y = -2y.
7. 16x + 2y
Collect x terms: 8x + 8x = 16x. Collect y terms: 5y − 3y = 2y.
8. 10x + 5y
Collect x terms: 5x + 5x = 10x. Collect y terms: 6y − 1y = 5y.
9. 10x + 2
Multiply each term inside by 2. 2 × 5x = 10x, 2 × 1 = 2.
10. 10x + 18
Multiply each term inside by 2. 2 × 5x = 10x, 2 × 9 = 18.
11. 15x + 45
Multiply each term inside by 5. 5 × 3x = 15x, 5 × 9 = 45.
12. 24x + 20
Multiply each term inside by 4. 4 × 6x = 24x, 4 × 5 = 20.
Worked examples
Find the value of 5x + 20 when x = 6.
- Replace x with 6: 5 × 6 + 20.
- 30 + 20 = 50.
- Answer: 50
Simplify 2x + 5y + 6x − 7y.
- Collect x terms: 2x + 6x = 8x.
- Collect y terms: 5y − 7y = -2y.
- Answer: 8x − 2y
Expand 3(3x + 4).
- Multiply each term inside by 3.
- 3 × 3x = 9x, 3 × 4 = 12.
- Answer: 9x + 12
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
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Frequently asked
- Is this Grade 3 Working with Expanding Double Brackets flashcards really free?
- Yes. Every flashcards 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 Introducing Expanding Double Brackets, Sequences. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Working with Expanding Double Brackets?
- Move on to Expanding Double Brackets in Context, Factorising Quadratics, Completing the Square, The Quadratic Formula, which build directly on this idea.
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