Page 1: Quadratic Expressions and Factorisation

This page introduces the fundamental concepts of quadratic expressions and their manipulation through expansion and factorisation. The content focuses on methods for expanding bracket expressions and factorising quadratic terms.

Definition: Quadratic expressions are algebraic expressions where the highest power of a variable is 2, such as y² or 3t².

Example: When expanding (x + 3)(x + 4), multiply each term in the first bracket by each term in the second bracket.

Highlight: For factorisation of expressions like x² + ax + b, the expression inside each bracket will start with x, and the signs in the brackets depend on the original expression's signs.

Vocabulary: Factorisation is the process of converting a quadratic expression back into its bracket form.

The page outlines different patterns for factorising quadratic expressions:

• x² + ax + b = (x + ?)(x + ?)
• x² + ax - b = (x + ?)(x - ?)
• x² - ax + b = (x - ?)(x - ?)