Collect like terms and simplify products and quotients of algebraic terms so expressions are as short as possible. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Simplifying is collecting like with like. 7b and 10b are the same type of term, so 7b−10b=−3b. 2x2 and −x2 are like each other, but they are not like 3x. Collect the x2 pile and the x pile separately: 2x2+3x−x2+5x=x2+8x.
For products and quotients, multiply or divide the numbers and use the index laws on matching letters. 6ab÷2b=3a, because 6÷2=3 and one b cancels. You cannot cancel a + or a − through a fraction — only factors.
An expression is not an equation. Do not put '=0' on the end unless you are solving. The simplified expression is the answer.
Objectives
4x and 3x are like terms. 4x and 3 are not.
The coefficient is the number in front of the letter.
4x + 3x = 7x. The letter stays.
Key points
Recognise like terms (same letter, same power) and collect them.
Keep the sign in front of each term with the term when collecting.
Simplify products such as 3p×4q and a×a×a.
Simplify quotients such as 12m÷3 and 6ab÷2b.
Worked examples
Example 1
Simplify 2x + 3x.
1 marks
2x and 3x are like terms, because both have the letter x.
Add the coefficients: 2 + 3 = 5.
The result is 5x.
Answer: 5x
Common slips
Slip: 4x and 3x are like terms, because both have the letter x. That changes a number from the question, so it answers a different question.
Slip: Add the coefficients: 5 + 3 = 5. That changes a number in the working, so the step no longer follows from the one before.
Slip: The result is 9x. That does not match the working above it.
Example 2
Simplify 2y + 2 + 4y + 1.
2 marks
Collect the y terms: 2 + 4 = 6, so 6y.
Collect the numbers: 2 + 1 = 3.
The result is 6y + 3.
Answer: 6y + 3
Common slips
Slip: Collect the y terms: 4 + 4 = 6, so 6y. That changes a number from the question, so it answers a different question.
Slip: Collect the numbers: 5 + 1 = 3. That changes a number in the working, so the step no longer follows from the one before.
Slip: The result is 10y + 3. That does not match the working above it.
Example 3
Simplify 4p + 2q − 2p.
2 marks
Collect the p terms: 4p − 2p = 2p.
The 2q term has no like term, so it stays as 2q.
The result is 2p + 2q.
Answer: 2p + 2q
Common slips
Slip: Collect the p terms: 6p − 2p = 2p. That changes a number from the question, so it answers a different question.
Slip: The 5q term has no like term, so it stays as 2q. That changes a number in the working, so the step no longer follows from the one before.
Slip: The result is 6p + 2q. That does not match the working above it.
Questions and answers
GCSE Maths simplifying algebra questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Simplify 3x + 6x.
Show answer
Answer: 9x
3x and 6x are like terms, because both have the letter x.
Add the coefficients: 3 + 6 = 9.
M1 — 3x and 6x are like terms, because both have the letter x.
A1 — Answer 9x
Question 2 Easy2 marks
Simplify 3y + 3 + 7y + 2.
Show answer
Answer: 10y + 5
Collect the y terms: 3 + 7 = 10, so 10y.
Collect the numbers: 3 + 2 = 5.
M1 — Collect the y terms: 3 + 7 = 10, so 10y.
A1 — Answer 10y + 5
Question 3 Medium2 marks
Simplify 4y + 4 + 10y + 3.
Show answer
Answer: 14y + 7
Collect the y terms: 4 + 10 = 14, so 14y.
Collect the numbers: 4 + 3 = 7.
M1 — Collect the y terms: 4 + 10 = 14, so 14y.
A1 — Answer 14y + 7
Question 4 Medium2 marks
Simplify 8p + 4q − 4p.
Show answer
Answer: 4p + 4q
Collect the p terms: 8p − 4p = 4p.
The 4q term has no like term, so it stays as 4q.
M1 — Collect the p terms: 8p − 4p = 4p.
A1 — Answer 4p + 4q
Question 5 Hard2 marks
Simplify 7p + 5q − 5p.
Show answer
Answer: 2p + 5q
Collect the p terms: 7p − 5p = 2p.
The 5q term has no like term, so it stays as 5q.
M1 — Collect the p terms: 7p − 5p = 2p.
A1 — Answer 2p + 5q
Question 6 Hard2 marks
Simplify 6x + 15x.
Show answer
Answer: 21x
6x and 15x are like terms, because both have the letter x.
Add the coefficients: 6 + 15 = 21.
M1 — 6x and 15x are like terms, because both have the letter x.
A1 — Answer 21x
Question 7 Exam-style2 marks
Simplify 7p + 2q − 3p.
Show answer
Answer: 4p + 2q
Collect the p terms: 7p − 3p = 4p.
The 2q term has no like term, so it stays as 2q.
The result is 4p + 2q.
M1 — Collect the p terms: 7p − 3p = 4p.
A1 — Answer 4p + 2q
Common mistakes
Most lost marks on this topic are one slip.
Adding the letters to make x².
Adding like terms changes the coefficient, not the power.
Adding a number onto the coefficient.
4x + 3 is already simplified.
Collecting different letters into one term.
Keep each letter in its own term.
Spot the slip
Which terms can be added to 4x?
3x
3
3y
Show the slip
3x Like terms use the same letter.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Circle each term with its sign before you start; it is the quickest way to avoid sign errors.
Do not write 1x or x1 in a final answer — write x.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.