Expand simple parentheses and collect like terms
Distribute a factor across every term · Collect matching variable powers · Use an equivalent expression in context
Section E2.8 · Extended · Expanding and collecting terms
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Terms and coefficients
- Signed arithmetic
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Distribute a factor across every term
- Collect matching variable powers
- Use an equivalent expression in context
Distribute to every term
a(b+c) = ab+ac. A negative outside multiplier changes every inside term's sign as well as its magnitude. For −2(4x−3), the result is −8x+6, not −8x−3.
Collect only like terms
Like terms have the same variables at the same powers. 3x+5x = 8x, but 3x+5x² cannot be combined into one term. Expanding and simplifying preserve the expression for every allowed input; check a substituted value to detect a sign error.
Sources for this lesson
Pause and explain
What is −2(4x−3)?
Worked example
Expand and simplify 4(3x−2)−5x.
Show the worked solution
- Distribute: 12x−8−5x.
- Collect x terms to obtain 7x−8.
Answer 7x−8.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Simplify 3(2x+4)+x.
Give me a hint
Expand before collecting.
Compare my reasoning
- 6x+12+x.
- Collect to 7x+12.
7x+12.
Look for these in your work
- Distribute fully
- Collect like terms
Simplify −2(4a−3b)+5a.
Give me a hint
Track the outside negative multiplier.
Compare my reasoning
- −8a+6b+5a.
- Collect a terms to obtain −3a+6b.
−3a+6b.
Look for these in your work
- Check signs
- Do not combine unlike variables
A rectangle has sides 3x+2 and x−1, with x > 1. Form and simplify its perimeter.
Give me a hint
Use twice the sum of the adjacent sides.
Compare my reasoning
- P = 2[(3x+2)+(x−1)].
- P = 2(4x+1) = 8x+2.
P = 8x+2, on x > 1.
Look for these in your work
- Model the perimeter first
- Keep the physical domain
Common mistakes
- Distribute across every term.
- Different powers are not like terms.
What can you explain now?
What is −2(4x−3)?
Compare with the explanation
−8x+6.
The product of the two negative signs makes the constant positive.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What is −2(4x−3)?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.