Expanding, Factorising and Simplifying
Create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties.
Expanding and factorising are the same move in opposite directions. Once you see that, factorising stops being guesswork.
Builds onYr 7 · Expanding Brackets
Method
Expanding removes brackets
Multiply every term inside by what is outside.
Factorising puts them back
Take out the highest common factor.
Watch a minus outside the bracket
It changes the sign of every term inside.
Collect like terms last
Expand first, then gather. Never both at once.
Worked example
e.g.
- Expand the first bracket.
- Expand the second. The minus outside changes both signs.
- Write it all out with no brackets.
- Collect the terms.
- Collect the numbers.
- Write the answer.
Practice
Expand fully before collecting. Take each sign with its term.
1
Answer
2
Answer
3
Answer
4
Answer
5
Answer
6
Answer