Collecting like-terms
Collecting like terms means combining parts of an expression that are the same. For example, 3a3a3a and 5a5a5a are like terms, so they can be added together to make 8a8a8a. By grouping the like terms carefully, we can simplify expressions and make them easier to work with. Jump to the questions
Practise now
Topic guide
What this worksheet practises
This worksheet provides practice on simplifying algebraic expressions by "collecting like terms". This means gathering together the parts of an expression that are the same type (e.g., grouping all the 'x's together and all the 'y's together) to make the maths much shorter.
Key method
You can only add or subtract terms if they have the exact same letter(s).
- Look at the expression. Identify the different "families" of terms (e.g., the 'x' family, the 'y' family, and the normal number family).
- Focus on one family at a time. Highlight or circle all the terms in that family.
- Crucial Step: Whenever you highlight a term, you must include the + or − sign immediately in front of it. That sign belongs to the term.
- Add or subtract the numbers in front of the letters for that family.
- Write out the simplified final expression.
Worked example
Simplify 5a + 3b − 2a + 4b + 7
Step 1: Identify the families. We have 'a's, 'b's, and normal numbers.
Step 2: Collect the 'a' family. We have 5a and − 2a.
5a − 2a = 3a.
Step 3: Collect the 'b' family. We have + 3b and + 4b.
3b + 4b = +7b.
Step 4: Collect the normal numbers. We only have + 7.
Step 5: Write the final simplified expression by pushing them all together.
The final answer is 3a + 7b + 7.
Common mistakes to avoid
The most common mistake is ignoring the negative signs. In the example above, a student might see the '5a' and the '2a', and just add them together to get '7a', completely missing the minus sign attached to the front of the 2a. Always circle the sign along with the term.
Things to remember
Different powers of the same letter belong to completely different families. You cannot add an x² to a normal x. So, 3x² + 4x cannot be simplified any further. They are not "like terms".