Simplifying expressions involves combining like terms to write algebra in its simplest form. This is a core GCSE Maths skill used in equations, expanding brackets and factorising.
Simplifying expressions means rewriting an algebraic expression in its simplest form by combining like terms.
In GCSE Maths, this usually involves adding or subtracting terms with the same variables, such as \(3x\) and \(5x\), while keeping different terms separate. This skill is essential before expanding brackets and factorising expressions.
Like terms have the same variables raised to the same power, for example \(3x\) and \(7x\).
To simplify an expression, combine the coefficients of like terms while keeping the variable the same.
This process is often used when solving linear equations.
Terms that are not alike, such as \(x\) and \(y\), cannot be combined and must stay separate.
Always pay attention to negative signs, as they can change the result when combining terms.
A mathematical phrase made up of numbers, variables and operations, without an equals sign. For example, \(3x + 5\).
A single part of an expression, separated by addition or subtraction signs. For example, in \(3x + 5\), the terms are \(3x\) and \(5\).
The numerical value that multiplies a variable. For example, in \(5x\), the coefficient is 5.
A letter used to represent an unknown or changing value, such as \(x\) or \(y\).
Terms that have exactly the same variables raised to the same powers, such as \(3x\) and \(7x\). Only like terms can be combined when simplifying expressions.
To rewrite an expression in its simplest form by combining like terms and removing unnecessary parts, without changing its value. This is used before expanding brackets and factorising.
Terms can only be added or subtracted if they have the same variables raised to the same powers. For example, \(3x + 4x = 7x\).
Terms with different variables or powers cannot be combined. For example, \(3x + 4y\) stays as it is.
When combining like terms, only the numbers (coefficients) are added or subtracted. The variable part stays the same, for example \(5a - 2a = 3a\).
Negative signs affect the value of terms. Always include the sign when combining, for example \(7x - 10x = -3x\).
\(2x + 9x\) → same variable
\(2x + 9\) → variable and number
\(4ab - ab\) → same variables
\(4a + 4a^2\) → different powers
Simplifying expressions means rewriting algebra in a neater form without changing its value. For GCSE Maths, this usually means collecting like terms.
Like terms have the same variables raised to the same powers. Only the coefficients change when they are combined.
A term is one part of an expression. Keep the sign in front of each term, because the sign belongs to that term.
Put terms with the same variable and power together. Constants can also be grouped together.
Add or subtract the coefficients of like terms. The variable part stays the same.
Terms with powers can only be combined when the powers match exactly.
\(5x^2 + 2x^2 = 7x^2\)
\(5x^2 + 2x\)
If an expression includes brackets, use expanding brackets first, then collect like terms.
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on collecting like terms and simplifying expressions accurately.
Simplify:
\(3x + 5x\)
Simplify:
\(7a - 2a\)
Simplify:
\(4y + 3 - y + 8\)
Simplify:
\(6p - 2q + 3p + 5q\)
Simplify fully:
\(5x + 2y - 3x + 4y\)
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on algebraic fluency, signs and unlike terms.
Simplify:
\(3a + 4b - 2a + b\)
Simplify:
\(8x - 3 + 2x + 7\)
Simplify fully:
\(5m + 3n - 2m + 6n\)
Simplify:
\(9p - 4q - 2p + q\)
A student writes:
\(4x + 3y = 7xy\)
Explain why this is incorrect.
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning, powers and algebraic precision.
Simplify:
\(6x + 4 - 2x + 9\)
Simplify:
\(3a + 2b + 5a - 7b\)
Simplify fully:
\(4x + 3y - 2x - y + 6\)
Simplify:
\(2p + 3q - 5 + 4p - q + 2\)
Explain why only like terms can be combined when simplifying algebraic expressions.
Identify each term in the expression, including the sign in front of it.
Group like terms with the same variables and powers.
Combine the coefficients only, keeping the variable part unchanged.
Simplify constants separately and write the final expression neatly.
Check signs, variables and powers before giving your final answer.
These are the mistakes students most often make when simplifying algebraic expressions.
\(3x + 2 = 5x\)
\(3x + 2\) cannot be simplified further because \(3x\) and \(2\) are not like terms.
\(7x - 10x = 3x\)
\(7x - 10x = -3x\). The minus sign must be included.
\(4x + 3x^2 = 7x^2\)
\(x\) and \(x^2\) are different powers, so they cannot be combined.
\(5a + 2a = 7a^2\)
\(5a + 2a = 7a\). Only the coefficient changes.
\(2(x+3)+x = 2x + 3 + x\)
\(2(x+3)+x = 2x + 6 + x = 3x + 6\).
Practise collecting like terms, handling negative signs and writing algebraic expressions in their simplest form.
Start by collecting simple like terms, constants and negative terms.
Simplify: \(7a + a - 5a\)
Simplify: \(9x - 4x\)
Simplify: \(3m + 5n + 2m\)
Simplify: \(6p + 4 - 2p\)
Which expression simplifies to \(8y\)?
Simplify: \(10a - a - 3a\)
Simplify: \(4x + 7 + 3x - 2\)
Simplify: \(8b + 3c - 5b + c\)
A student says \(2x + 5 = 7x\). What is the mistake?
Simplify: \(12q - 4 + 2q - 9\)
Collect powers, products, negatives and mixed algebraic terms.
Simplify: \(5x^2 + 3x - 2x^2 + 4x\)
Simplify: \(7a^2 - 3a + 2a^2 + 8a\)
Simplify: \(6ab + 4a - 2ab + 7a\)
Simplify: \(9m - 4n - 6m + 10n\)
Which expression simplifies to \(2x^2 - 5x\)?
Simplify: \(4t^2 + 6t - 9 + 3t^2 - 2t + 5\)
A student simplifies \(3x^2 + 4x\) to \(7x^2\). What mistake have they made?
Simplify: \(11xy - 4x + 3xy + 9x\)
Simplify: \(2a - 3b - 5a + 8b - 4\)
Simplify: \(8p^2 - 3pq + 5p^2 + 7pq - 6p\)
Practise this topic with interactive games.
Like terms are terms that have the same variables raised to the same powers. For example, \(3x\) and \(7x\) are like terms, but \(3x\) and \(3y\) are not.
To simplify an algebraic expression, group like terms together and add or subtract their coefficients. Keep the variables the same and write the final expression in its simplest form.
No, unlike terms cannot be combined. Terms with different variables or different powers, such as \(x\) and \(x^2\), must stay separate.
Simplifying expressions is a key GCSE Maths skill used in solving equations, expanding brackets and factorising. It helps make algebra easier to work with and reduces mistakes in calculations.
Common mistakes include combining unlike terms, forgetting negative signs, and mixing up variables with different powers such as \(x\) and \(x^2\).