GCSE specification fit
A core algebra skill before brackets, equations and graphs.
Simplifying expressions means writing algebra in a shorter, clearer form without changing its value. It is used throughout GCSE algebra.
What you will learn
Why this matters
GCSE questions often hide the main idea behind untidy algebra. Simplifying first makes later steps easier to read and reduces the chance of sign mistakes.
It also helps examiners follow your work. A neat simplified expression can earn method marks even when a longer problem continues afterwards.
Prior knowledge
You should already be comfortable with:
Clear explanation
Like terms
Like terms have exactly the same variable part. The coefficients can be different, but the letters and powers must match.
Collecting like terms
To collect like terms, keep the variable part the same and combine the coefficients.
You can also collect several groups of like terms in the same expression.
Keep the sign with the term
A minus sign belongs to the term after it. Moving terms around is safer when you move the sign with them.
Unlike terms do not combine
The expression 3x + 4y is already simplified. The terms use different variables, so they cannot become 7xy or 7x.
3x + 4y stays as 3x + 4yMultiplying algebraic terms
When multiplying terms, multiply the numbers and multiply the variables.
If the same variable is repeated, use a power: x × x = x².
Checking by substitution
A simplified expression should have the same value as the original expression for every value of the variable. You can check with an easy number.
Worked examples
Example 1: Collect one type of term
Simplify 8x − 3x + 2x.
8x − 3x + 2x = 7xExample 2: Collect two types of term
Simplify 5a + 6b − 2a + b.
5a − 2a = 3a 6b + b = 7bExample 3: Keep negative signs attached
Simplify 4m − 9 + 7m − 2.
4m + 7m = 11m −9 − 2 = −11Example 4: Multiply algebraic terms
Simplify 6x × 3x.
6 × 3 = 18 x × x = x²Quick checks
Choose an answer, then check your thinking.
1. Which pair are like terms?
2. Simplify 9p − 4p.
3. Simplify 2x × 5x.
Practice questions
Question 1
A pupil has 6x counters and then adds 4x more. Write the total as a simplified expression.
Reveal answer and marking guidance
Answer: 10x.
Marking: Add the coefficients 6 and 4, then keep x.
Question 2
A length of 5a is cut from a strip of length 12a. Write the remaining length as a simplified expression.
Reveal answer and marking guidance
Answer: 7a.
Marking: 12 lots of a minus 5 lots of a leaves 7 lots of a.
Question 3
Collect the like terms in 3p + 2q + 5p − q, keeping the p terms and q terms separate.
Reveal answer and marking guidance
Answer: 8p + q.
Marking: 3p + 5p = 8p and 2q − q = q.
Question 4
Simplify 7m − 4 − 2m + 9, making sure the negative sign stays attached to the term it belongs to.
Reveal answer and marking guidance
Answer: 5m + 5.
Marking: 7m − 2m = 5m and −4 + 9 = 5.
Question 5
A rectangle has side lengths 4a and 3b. Write an expression for its area in simplest form.
Reveal answer and marking guidance
Answer: 12ab.
Marking: 4 × 3 = 12 and a × b = ab.
Question 6
Simplify −3x × 5x.
Reveal answer and marking guidance
Answer: −15x².
Marking: −3 × 5 = −15 and x × x = x².
Question 7
Simplify 4x² + 3x − 7 + 2x² − 5x + 11.
Reveal answer and marking guidance
Answer: 6x² − 2x + 4.
Marking: Collect each type separately: 4x² + 2x² = 6x², 3x − 5x = −2x and −7 + 11 = 4.
Question 8
Simplify 2ab + 5a − 3ab + 4b − a.
Reveal answer and marking guidance
Answer: −ab + 4a + 4b.
Marking: 2ab − 3ab = −ab, 5a − a = 4a and 4b has no other like term.
Question 9
Simplify 6x² − 4xy + 9x − 2x² + 7xy − 5x.
Reveal answer and marking guidance
Answer: 4x² + 3xy + 4x.
Marking: Collect each term type separately: 6x² − 2x² = 4x², −4xy + 7xy = 3xy and 9x − 5x = 4x.
Question 10
Simplify 5a²b − 3ab² + 2a²b + 7ab² − 4ab.
Reveal answer and marking guidance
Answer: 7a²b + 4ab² − 4ab.
Marking: Collect only matching variable parts: 5a²b + 2a²b = 7a²b, −3ab² + 7ab² = 4ab², and −4ab has no like term.
Answers and marking guidance
The exact practice answers are hidden under each question so you can try first. For simplifying expressions, marks usually come from collecting only like terms, carrying the sign with each term, multiplying coefficients and variables carefully, and checking by substituting a simple value if two expressions are meant to be equivalent.
Common mistakes
- Combining unlike terms: 3x + 2y cannot become 5xy.
- Losing the variable: 6a + 4a = 10a, not 10.
- Dropping negative signs: in 5x − 8x, the second term is −8x.
- Adding powers when collecting: x + x = 2x, not x².
- Forgetting powers when multiplying: x × x = x².
Extension challenge
Simplify 4a + 3b − 7a + 2b + 5ab − 2ab.
Reveal answer
Answer: −3a + 5b + 3ab.
Collect each type of term separately: 4a − 7a = −3a, 3b + 2b = 5b and 5ab − 2ab = 3ab.
Exam-board guidance
Simplifying expressions questions test whether you can collect only matching term types, keep signs attached and write a tidy line before later algebra such as brackets, equations or formulae.
AQA GCSE Maths
Collect only matching variable parts before solving, substituting or factorising, and keep unlike terms such as x and x² separate.
OCR GCSE Maths
Keep the sign attached to each term, especially when rearranging terms such as 7m − 4 − 2m + 9.
Pearson Edexcel GCSE Maths
Group each term type in one clear line so the examiner can see constants, x terms and squared terms have been handled separately.
Eduqas GCSE Maths
Check the full variable part before combining terms; ab, a and b are three different term types.
WJEC Wales
Simplify the algebra before interpreting a formula or numeracy context, and do not drop units once values are substituted later.
CCEA GCSE Maths
Simplify before equation solving and check signs carefully, because one lost negative can affect several later marks.
Next lesson
Next, move into Expanding Brackets.