Learning Objectives
- Explain what like terms are.
- Identify like and unlike terms.
- Simplify algebraic expressions by collecting like terms.
- Avoid one of the most common Algebra mistakes.
Introduction
This lesson develops Collecting Like Terms from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🎬 Group only like terms
Only terms with the same variable part can combine.
🤔 Think About This...
Imagine you empty your school bag onto your bed. You have:
- 3 Maths books
- 2 English books
- 4 Maths books
- 1 English book
Would you leave everything mixed together? Probably not. You would put the Maths books together and the English books together.
English Books 2 + 1 = 3
That is exactly what collecting like terms means.
📖 What are Like Terms?
Like terms are terms that have exactly the same variable.
For example:
Both have the variable x, so they are like terms.
These are also like terms.
❌ Unlike Terms
These cannot be combined.
Example
Why?
One has x. One has y. Different variables.
📝 Worked Examples
Example 1
Simplify:
Thinking...
Both terms contain x. Add the numbers.
Example 2
Both terms contain a. Subtract the coefficients.
Example 3
Group like terms.
🌍 Real-Life Example
Imagine one loaf of bread costs x dollars. You buy:
- 3 loaves today
- 2 loaves tomorrow
Total cost:
Collect like terms.
Practice Questions
- 4x + 3x
- 9a − 4a
- 7y + 2 + y
- 6m + 5m − 3
- 10x − 2x + 5
✅ Show Answers
- 7x
- 5a
- 8y + 2
- 11m − 3
- 8x + 5
🧠 Did You Know?
⭐ What You Can Do Now
- ✅ I can identify like terms.
- ✅ I know why unlike terms cannot be combined.
- ✅ I can simplify simple expressions.
🎉 Well Done!
You've learned one of the most important Algebra skills. Every topic from here onwards will use collecting like terms.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
📈 Your Progress
Lesson 4 of 22
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.