This worksheet builds algebraic fluency, teaching students to expand, factorise, rearrange and simplify linear expressions using the distributive and associative properties. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Expanding uses the distributive property: a(b + c) = ab + ac — multiply everything inside the brackets by what's outside.
- Factorising is the reverse of expanding: find the highest common factor of every term, then write it outside a bracket.
- Like terms (same variable, same power) can be combined by adding or subtracting their coefficients.
- A negative sign outside brackets flips the sign of every term inside when expanded, e.g. −2(x + 3) = −2x − 6.
- Expanding and factorising are inverse operations — factorising a correctly expanded expression should return the original.
What your child will practise:
- Expanding brackets by multiplying every term inside by the term outside.
- Combining like terms after expanding to simplify an expression fully.
- Factorising an expression by finding the highest common factor of all its terms.
- Expanding two or more bracketed terms and then combine like terms across the whole expression.
- Checking a factorisation by re-expanding it and confirming it matches the original expression.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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