Factorising Algebraic Expressions

Overview

• Objective: Understand the process of factorising algebraic expressions.
• Importance: Essential skill in simplifying expressions and solving equations.

Key Concepts

• Factorisation: The process of breaking down an expression into a product of simpler expressions.
• Common Factors: Identifying common elements in terms to simplify expressions.
• Difference of Squares: A particular factorisation technique useful for expressions in the form (a^2 - b^2).

Steps in Factorising

1. Identify and extract common factors: Simplify expressions by factoring out the greatest common factor.
2. Use special formulae: Apply identities like (a^2 - b^2 = (a + b)(a - b)).
3. Rearrange and simplify: Simplify complex expressions using factorisation techniques.

Practice Problems

• Factorise the following:
  • (x^2 - 9)
  • (4x^2 - 12x)

Applications

• Simplifying Expressions: Reduce complexity and make computations easier.
• Solving Equations: Transforming equations into a solvable form by factorisation.

Further Reading

• Review more complex factorisation methods for complex expressions.
• Explore how factorisation relates to polynomial division and remainder theorem.

Note: The lecture may also include a PowerPoint presentation with additional examples and visual aids.

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