Page 2: The FOIL Method for Double Brackets

This page explains the systematic FOIL method for expanding double brackets, providing a structured approach to multiplication of binomial expressions.

Definition: FOIL stands for First, Outside, Inside, Last - representing the order of multiplication when expanding double brackets.

Example: When expanding $x + 3$$x + 8$:

• First: x × x = x²
• Outside: x × 8 = 8x
• Inside: 3 × x = 3x
• Last: 3 × 8 = 24
• Combined result: x² + 11x + 24

Highlight: Double bracket expansion typically results in four terms initially, often combining to three terms after simplification.

Page 3: Squared Brackets

This page covers the special case of squared brackets and demonstrates how to handle them in algebraic expressions.

Definition: A squared bracket $a + b$² is equivalent to $a + b$$a + b$ and should be expanded as such.

Example: For $3x + 2$²:

• Rewrite as $3x + 2$$3x + 2$
• Apply FOIL method
• Result: 9x² + 12x + 4

Highlight: Always rewrite squared brackets as double brackets before expanding to ensure accurate results.

Page 1: Basic Bracket Expansion

This page introduces the fundamental concept of expanding single brackets in algebraic expressions. The process involves multiplying each term inside the brackets by the term outside.

Definition: Expanding brackets means multiplying each term inside the brackets by the term outside the brackets.

Example: In expanding 3$2x + 5$:

• First multiply 3 × 2x = 6x
• Then multiply 3 × 5 = 15
• Final answer: 6x + 15

Highlight: When expanding multiple brackets in one expression, expand each bracket separately first, then group like terms, and finally simplify the expression.

Vocabulary: Like terms are terms that have the same variables raised to the same powers.