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 Cambridge Lower Secondary curriculum. This topic involves two main processes: expansion and factorisation.

Expansion refers to 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 essentially the reverse process of expansion. It involves taking out the common factor from terms. For instance, in the expression $8x^2y + 6xy^2$, the common factor is $2xy$, resulting in $2xy(4x + 3y)$.

To simplify algebraic expressions, combine like terms by grouping variables with the same powers. For example, in the expression $x^3 + 3x^2 - 2x^3 + 2x - x^2 + 3$, combining like terms results in $-x^3 + 2x^2 + x + 3$.

Exam Tips

• Understand the Basics: Ensure you are comfortable with identifying like terms and common factors. This is crucial for both expansion and factorisation.
• Practice Pairing Terms: Sometimes, dividing terms into pairs can simplify the factorisation process, as seen in expressions like $18mx - 3nx + 12my - 2ny$.
• 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. Practice with expressions like $(3x^2 - 5x) - (x^2 - 2x + 2)$ to see the principles in action.
• Stay Organized: Write each step clearly to avoid confusion, especially when dealing with complex expressions.