Page 2: Double Distributivity and Advanced Applications

The second page delves into more advanced concepts, particularly double distributivity and its applications.

Example: C = (3x + 2)(5x + 6) = 15x² + 18x + 10x + 12 = 15x² + 28x + 12

This example illustrates the process of double distributivité (double distributivity), showing how to multiply two binomials.

Highlight: When applying double distributivity, multiply each term of the first parenthesis by each term of the second parenthesis.

The page also covers special cases, such as when the development is preceded by a minus sign:

Example: D = -(3x + 2)(5x - 6) = -15x² + 18x - 10x + 12 = -15x² + 8x + 12

This demonstrates how to handle negative signs in front of parentheses during distribution, which is crucial for supprimer les parenthèses puis réduire les expressions suivantes (removing parentheses and then reducing the following expressions).

The page concludes with important definitions:

Definition: • Développer (Develop): Express an expression as a sum (or difference) of several terms. • Réduire (Reduce): Write an expression using the least number of terms possible. • Ordonner (Order): Write an expression in decreasing order of the variable's power.

These definitions are essential for mastering algebraic manipulations and are particularly useful for exercises like réduire une expression littérale 4ème (reducing a literal expression in 4th grade) and double distributivité 3ème (double distributivity in 3rd grade).

Page 1: Removing Parentheses and Basic Algebraic Operations

The first page introduces fundamental algebraic operations, focusing on removing parentheses and simplifying expressions.

Example: A = 3 - (5 - 2) = 3 - 5 + 2 = x - 2

This example demonstrates how to remove parentheses by changing the sign of the terms inside when preceded by a minus sign.

Highlight: When removing parentheses preceded by a minus sign, change the signs of all terms inside.

The page also covers basic literal calculations and reducing expressions.

Example: A = 5(x + 3) = 5x + 15

This shows the application of the distributive property, a key concept in algebraic manipulation.

Vocabulary: Réduire une expression littérale (Reducing a literal expression) involves combining like terms to simplify an algebraic expression.

The page concludes with an introduction to simple distributivity, presenting the general rules:

Definition: Simple distributivity rules: • k(a + b) = ka + kb • k(a - b) = ka - kb

These rules form the basis for more complex algebraic operations and are essential for suppression des parenthèses exercices corrigés (solved exercises on removing parentheses).