Algebraic Operations and Distributivity

This page focuses on calcul littéral (literal calculation) and the concept of distributivity in algebra. It covers simple and double distributivity, providing examples and exercises to reinforce understanding.

Definition: Distributivity is a property of operations that allows the multiplication of a number over a sum.

Key concepts covered:

1. Simple Distributivity: k(a + b) = ka + kb

   Example: 5(x + 4) = 5x + 20

2. Double Distributivity: (a + b)(c + d) = ac + ad + bc + bd

   Example: (x + 3)(2 - x) = 2x + 6 - x² - 3x = -x² + 2x + 6

The page also includes an area calculation problem that applies algebraic concepts:

Example: Calculate the shaded area of a square with side length 5, where a smaller square with side length (x + 3) is removed from one corner.

Solution:

• Area of large square: 5 × 5 = 25
• Area of small square: (x + 3)²
• Shaded area: 25 - (x + 3)²

Highlight: This page provides excellent practice for distributivité simple exercices and introduces more complex algebraic manipulations, which are essential for students studying calcul littéral 3ème.