This section delves into simple and double distribution properties, providing essential formulas and practical applications in algebraic operations.

Definition: Simple distributivity is expressed as K$a + b$ = Ka + Kb, where K is distributed to each term inside the parentheses.

Example: C = 5$4-x$ simplifies to C = 20-5x through simple distribution.

Highlight: Double distributivity follows the pattern $a + b$$c + d$ = ac + ad + bc + bd.

Vocabulary: "Factorisation" refers to the reverse process of distribution, where common factors are extracted.

The page illustrates these concepts through detailed examples:

• Simple distribution: C = 5$4-x$ → C = 20-5x
• Double distribution: E = $x+2$$3x-1$ → E = 3x² + 5x - 2

A final note introduces factorization as the inverse operation: Ka + Kb = K$a + b$

This section explores the fundamental rules of working with signs and parentheses in algebraic expressions. The content focuses on how positive and negative signs affect terms within parentheses and demonstrates proper reduction techniques.

Definition: Reduction in algebra involves combining like terms to simplify expressions.

Example: In the expression 5+(4x), the positive sign before the parentheses maintains the signs within.

Highlight: When reducing expressions, always group similar terms: combine x terms with x terms, and x² terms with x² terms.

Vocabulary: "Réduire" (reduce) refers to the process of simplifying algebraic expressions by combining like terms.

The page demonstrates this through several worked examples:

• Expression A: 5+(4x) simplifies to 5+4x
• Expression B: 8+3x²$x+4$ reduces to 4+2x through careful application of distributive property

A comprehensive example shows how to reduce and group terms: 2x² + 3x - 5 + 8x² - 4x + 7 = 10x² - x + 2