Only collect like terms
What you will learn
Know the rule, then use it
These are the short notes. Read each one, then check you can use it in the worked example below.
Method
Like terms have exactly the same variable and power
Identify and group like terms
x² terms: 5x² and −2x²
Combine each group
x² terms: 5x² − 2x² = 3x²
Write the simplified expression
3x² − 4x + 5
Watch out
Students combine unlike terms, for example writing 3x² − 4x as −x²
Only collect terms with the same letter part.
Simplify 5x² + 3x − 2x² + 4 − 7x + 1
Identify and group like terms: x² terms: 5x² and −2x². x terms: 3x and −7x. Constants: 4 and 1.Grouping first reduces the chance of losing a term or its sign.
Combine each group: x² terms: 5x² − 2x² = 3x². x terms: 3x − 7x = −4x. Constants: 4 + 1 = 5.
Write the simplified expression: 3x² − 4x + 5. Convention is to write in descending powers of x.
3x² − 4x + 5
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
WorkedreasoningSimplify 5x² + 3x − 2x² + 4 − 7x + 1
3 marks4 minssimplifying-expressions-workedShow solution
Simplify 5x² + 3x − 2x² + 4 − 7x + 1
- 1.Identify and group like terms: x² terms: 5x² and −2x². x terms: 3x and −7x. Constants: 4 and 1.Grouping first reduces the chance of losing a term or its sign.
- 2.Combine each group: x² terms: 5x² − 2x² = 3x². x terms: 3x − 7x = −4x. Constants: 4 + 1 = 5.
- 3.Write the simplified expression: 3x² − 4x + 5. Convention is to write in descending powers of x.
3x² − 4x + 5
- M1: identify and group like terms
- M1: combine each group
- M1: write the simplified expression
- A1: 3x² − 4x + 5
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
DiagnosticrecallSimplify 4a + 3b − 2a + b
1 mark2 minssimplifying-expressions-q1Show solution
Simplify 4a + 3b − 2a + b
- 1.Spot the skill: Like terms have exactly the same variable and power.
- 2.Use the identify and group like terms stage first, then combine each group.
- 3.Keep the final answer visible: 2a + 4b.
2a + 4b
- M1: use the correct like terms have exactly the same variable and power. you can only combine them.think of it like sorting objects: x² terms go with x² terms, x terms with x terms, numbers with numbers — different 'species' cannot be mixed.
- A1: 2a + 4b
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
EasyprocedureSimplify 6x² − x + 3 − 2x² + 5x − 8
2 marks3 minssimplifying-expressions-q2Show solution
Simplify 6x² − x + 3 − 2x² + 5x − 8
- 1.Spot the skill: Like terms have exactly the same variable and power.
- 2.Use the combine each group stage first, then write the simplified expression.
- 3.Keep the final answer visible: 4x² + 4x − 5.
4x² + 4x − 5
- M1: use the correct like terms have exactly the same variable and power. you can only combine them.think of it like sorting objects: x² terms go with x² terms, x terms with x terms, numbers with numbers — different 'species' cannot be mixed.
- A1: 4x² + 4x − 5
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
MediumreasoningSimplify 2xy + 3x²y − xy + x²y
3 marks4 minssimplifying-expressions-q3Show solution
Simplify 2xy + 3x²y − xy + x²y
- 1.Spot the skill: Like terms have exactly the same variable and power.
- 2.Use the write the simplified expression stage first, then identify and group like terms.
- 3.Keep the final answer visible: 3x²y + xy.
3x²y + xy
- M1: use the correct like terms have exactly the same variable and power. you can only combine them.think of it like sorting objects: x² terms go with x² terms, x terms with x terms, numbers with numbers — different 'species' cannot be mixed.
- A1: 3x²y + xy
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
Hardproblem solvingSimplify (3x + 2) + (5x − 7) + (−2x + 4)
3 marks5 minssimplifying-expressions-q4Show solution
Simplify (3x + 2) + (5x − 7) + (−2x + 4)
- 1.Spot the skill: Like terms have exactly the same variable and power.
- 2.Use the identify and group like terms stage first, then combine each group.
- 3.Keep the final answer visible: 6x − 1.
6x − 1
- M1: use the correct like terms have exactly the same variable and power. you can only combine them.think of it like sorting objects: x² terms go with x² terms, x terms with x terms, numbers with numbers — different 'species' cannot be mixed.
- A1: 6x − 1
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
Exam-stylemulti-stepGiven that 5x + k and 3x + 8 simplify to 8x − 2 when added, find k.
4 marks6 minssimplifying-expressions-q5Show solution
Given that 5x + k and 3x + 8 simplify to 8x − 2 when added, find k.
- 1.Spot the skill: Like terms have exactly the same variable and power.
- 2.Use the combine each group stage first, then write the simplified expression.
- 3.Keep the final answer visible: k = −10.
k = −10
- M1: use the correct like terms have exactly the same variable and power. you can only combine them.think of it like sorting objects: x² terms go with x² terms, x terms with x terms, numbers with numbers — different 'species' cannot be mixed.
- A1: k = −10
g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
Grade 9 stretchproblem solvingSimplify 4x - 3(2x - 5) + x.
4 marks7 minssimplify-g9Show solution
Simplify 4x - 3(2x - 5) + x.
- 1.Expand the bracket carefully.
- 2.Collect the x terms and constants.
15 - x
- M1: obtain 4x - 6x + 15 + x
- A1: 15 - x
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Simplifying expressions - 2 marksSimplify 4a + 3b − 2a + bMark answer
2a + 4b
2Algebraic notation and substitution - 2 marksFind t² + 4t when t = −2Mark answer
−4
3Expanding and factorising - 2 marksFactorise x² − 7x + 12Mark answer
(x − 3)(x − 4)
4Linear equations - 3 marksSolve 3(2x − 1) = 2(x + 5)Mark answer
x =
- I can explain the method for simplifying expressions.
- I can show clear working without skipping key steps.
- g. writing 3x² − 4x as −x².These cannot be added because x² and x represent different quantities (squaring x gives a fundamentally different expression).Similarly, 3x + 4 cannot be simplified to 7x — the 4 is a constant, not an x term.If in doubt, substitute a value for x and check both expressions give the same number.
This guide follows the OCR GCSE Mathematics J560 specification. Practice questions are original Learnova questions shaped around official content and exam skills.