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 each term inside a bracket by the term outside, effectively distributing the multiplication across the terms. For example, expanding $(x + 1)(x + 2)$ results in $x^2 + 3x + 2$.
• Factorisation is the reverse process of expansion, where we 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 means 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 $-x^3 + 2x^2 + x + 3$.
• A useful tip for factorisation is to sometimes divide the terms into pairs to make the process easier, such as in $18mx - 3nx + 12my - 2ny$, which can be factorised to $(3x + 2y)(6m - n)$.

Exam Tips

• Identify Like Terms: Always start by identifying and combining like terms in an expression to simplify it effectively.
• Look for Common Factors: When factorising, search for the greatest common factor among the terms to simplify the process.
• Check Your Work: After expanding or factorising, re-expand or re-factorise to ensure accuracy.
• Practice Pairing: For complex expressions, practice dividing terms into pairs to simplify factorisation.
• Understand the Process: Grasp the concept that factorisation is the reverse of expansion, which will help in solving problems efficiently.