Développer et Réduire: A Comprehensive Guide

This page provides a detailed explanation of how to développer et réduire algebraic expressions, a crucial skill in mathematics. The process involves expanding products into sums and simplifying the resulting expression.

The document begins by defining the concept of developing an expression. Développer a product means transforming it into a sum (or difference) of terms. This is a fundamental operation in algebra, particularly important for solving equations and simplifying complex expressions.

Definition: Développer un produit consiste à transformer ce produit en sommes (+ ou -).

The page then presents two key formulas for developing expressions:

1. -k(a+b) = -ka - kb
2. (a + b)(c + d) = ac + ad + bc + bd

These formulas are essential for understanding how to expand different types of algebraic expressions.

Example: The document provides two practical examples to illustrate the process:

1. A = -5(x + 2) = -5x - 10
2. B = (4x - 1)(5 - 2x) = 20x² - 8x - 5x + 2 = 20x² - 13x + 2

These examples demonstrate how to apply the formulas in real algebraic situations, showing the step-by-step process of expanding and then combining like terms.

Highlight: The final step in both examples involves réduire, or simplifying the expression by combining like terms. This is a crucial part of the process, ensuring the final expression is in its most concise form.

Understanding how to développer et réduire expressions is fundamental for students progressing in algebra. It forms the basis for more advanced topics such as solving quadratic equations, factoring, and working with polynomials.

Vocabulary:

• Expression littérale: A mathematical expression containing both numbers and variables.
• Somme algébrique: The result of adding or subtracting algebraic terms.

This guide provides a solid foundation for students learning to développer et réduire une expression en ligne or tackle more complex exercices de développer et réduire. Mastering these skills is essential for success in mathematics courses from 3ème through 4ème and beyond.