Summary
In algebra, expansion involves multiplying out brackets to simplify expressions, while factorising is the process of breaking down an expression into a product of simpler expressions.
- Expansion — multiplying each term inside the bracket by the term outside. Example: (x + 1)(x + 2) becomes x^2 + 3x + 2.
- Factorising — taking out the common factor from terms. Example: 8x^2y + 6xy^2 becomes 2xy(4x + 3y).
- Like Terms — terms that have the same variables raised to the same power. Example: In 3x^2 + 2x^2, 3x^2 and 2x^2 are like terms.
Exam Tips
Key Definitions to Remember
- Expansion: Multiplying out brackets.
- Factorising: Taking out the common factor.
- Like Terms: Terms with the same variables and powers.
Common Confusions
- Mixing up expansion and factorising.
- Forgetting to combine like terms correctly.
Typical Exam Questions
- How do you expand (x + 1)(x + 2)? x^2 + 3x + 2
- Factorise 8x^2y + 6xy^2. 2xy(4x + 3y)
- Simplify 3x^2 + 2x^2. 5x^2
What Examiners Usually Test
- Ability to expand expressions correctly.
- Correctly factorising expressions by identifying common factors.
- Simplifying expressions by combining like terms.