Study Notes
Algebraic manipulation involves simplifying expressions, expanding brackets, and factorising expressions. It is essential to combine like terms and apply the distributive law for expansion.
- Like Terms — terms in an expression that have the same variable and power. Example: 5b + 3b = 8b
- Unlike Terms — terms in an expression that have different variables or powers. Example: 25x + 35y
- Expansion — multiplying each term inside a bracket by the term outside. Example: 2x(3x + y - 4z) = 6x^2 + 2xy - 8xz
- Factorisation — the process of writing an expression as a product of its factors. Example: 18mx - 3nx + 12my - 2ny = (3x + 2y)(6m - n)
- Quadratic Factorisation — factorising expressions of the form ax^2 + bx + c. Example: x^2 + 11x + 24 = (x + 3)(x + 8)
Exam Tips
Key Definitions to Remember
- Like Terms: Terms with the same variable and power
- Unlike Terms: Terms with different variables or powers
- Expansion: Distributing a term across terms inside a bracket
- Factorisation: Writing an expression as a product of factors
Common Confusions
- Mixing up like and unlike terms
- Forgetting to multiply each term inside the bracket during expansion
- Incorrectly identifying common factors in factorisation
Typical Exam Questions
- How do you simplify 3x^2 - x^2 + 2x - x + 3? Combine like terms: 2x^2 + x + 3
- What is the expanded form of (x + 1)(x + 2)? x^2 + 3x + 2
- How do you factorise x^2 + 11x + 24? (x + 3)(x + 8)
What Examiners Usually Test
- Ability to simplify expressions by combining like terms
- Correct application of the distributive law in expansion
- Skill in factorising quadratic expressions