Algebraic Calculations for Brevet Exam

This page introduces fundamental concepts in algebraic calculations, crucial for the French Brevet exam. It covers three main topics: reducing algebraic expressions, developing products, and the distributive property.

Reducing Algebraic Expressions

Reducing an algebraic sum involves decreasing the number of terms by combining like terms.

Definition: Reducing an algebraic sum means combining terms of the "same nature" to simplify the expression.

Example: 5x² - 3x² + 3x - 9x + 6x + 15 - 3 = 2x² + 0x + 12

Developing Products

Developing a product means transforming it into a sum using the distributive property.

Vocabulary: The distributive property is expressed as k(a + b) = ka + kb, where k is the factor of (a + b).

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

Highlight: For more complex expressions, the distributive property can be applied multiple times, as in B = 2x(4 + 3x) = 8x + 6x².

The page also covers the distributive property for subtraction: k(a - b) = ka - kb.

Example: D = -4x²(6x + 9) = -24x³ - 36x²

These calcul algébrique exercices corrigés Seconde provide a solid foundation for students preparing for the Brevet exam, offering clear explanations and examples of somme et produit exercices corrigés pdf.

Handling Parentheses in Algebraic Expressions

This page focuses on the rules for removing parentheses in algebraic expressions, an essential skill for simplifying equations.

Parentheses Preceded by a Plus Sign

When parentheses are preceded by a plus sign, they can be removed without changing the expression inside.

Rule: For expressions like a + (b + c), simply remove the parentheses: a + b + c.

Example: 5 + (2x + 3x - 4) = 5 + 2x + 3x - 4

This rule applies even in the absence of explicit development.

Parentheses Preceded by a Minus Sign

To remove parentheses preceded by a minus sign, change the sign of each term inside the parentheses.

Rule: For expressions like a - (b + c), remove the parentheses and change signs: a - b - c.

Example: 6x - (-2x - 3) = 6x + 2x + 3 = 8x + 3

These exercices suppression de parenthèses PDF are crucial for mastering calcul algébrique Seconde exercices corrigés PDF. Understanding the règle des parenthèses en Math is essential for solving more complex equations and preparing for exams like the Brevet.

Highlight: Proper handling of parentheses is a fundamental skill in algebraic calculations and is often tested in exercice type brevet maths avec corrigé.

This guide provides clear explanations and examples for supprimer les parenthèses puis réduire les expressions suivantes, which is a common type of question in exercice suppression de parenthèses 4e pdf.