Expansion and Factorising

Summary and Exam Tips for Expansion and Factorising

Expansion and Factorising is a subtopic of Algebra, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. This topic involves two main processes: expansion and factorisation.

• Expansion involves multiplying out expressions, such as distributing each term inside a bracket. For example, expanding $(x + 1)(x + 2)$ results in $x^2 + 3x + 2$.
• Factorisation is the reverse process, where you identify and extract common factors from terms. For instance, $8x^2y + 6xy^2$ can be factorised to $2xy(4x + 3y)$.
• Simplifying algebraic expressions requires combining like terms, which involves adding or subtracting terms with the same variables and powers. For example, simplifying $x^3 + 3x^2 - 2x^3 + 2x - x^2 + 3$ results in $-x^3 + 2x^2 + x + 3$.
• Sometimes, factorisation may require dividing terms into pairs to identify common factors, as seen in $18mx - 3nx + 12my - 2ny$, which simplifies to $(3x + 2y)(6m - n)$.

Exam Tips

• Understand the Basics: Make sure you are comfortable with identifying like terms and common factors. This is crucial for both expansion and factorisation.
• Practice Pairing: When factorising, practice dividing terms into pairs to make it easier to spot common factors.
• Check Your Work: After expanding or factorising, always recheck your work by reversing the process to ensure accuracy.
• Use Examples: Work through examples to solidify your understanding. This will help you recognize patterns and common mistakes.
• Stay Organized: Keep your work neat to avoid confusion, especially when dealing with complex expressions.