Developing Algebraic Expressions
This page focuses on the process of développer une expression (developing an expression) in algebra, which is a fundamental skill for students, particularly those studying développement maths 3ème (math development in 9th grade).
The main concept introduced is the distributive property, which is used to expand expressions containing parentheses. This property is essential for développer une expression exemple (developing an expression example) and solving more complex mathematical problems.
Definition: The distributive property states that a(b + c) = ab + ac. This means that when multiplying a term by a sum inside parentheses, you multiply the term by each element inside the parentheses.
Example: To développer une expression exemple, consider 5(x + 4):
5(x + 4) = 5 × x + 5 × 4 = 5x + 20
The page also introduces a more complex case of distribution with two binomials:
Formula: a + b(c + d) = ac + ad + bc + bd
Example: (x + 3)(2 + x) = x × 2 + x × x + 3 × 2 + 3 × x = 2x + x² + 6 + 3x = x² + 5x + 6
A special case is highlighted for squaring binomials:
Highlight: (a + b)² = a² + 2ab + b²
This formula is particularly useful for quickly développer une expression Seconde (developing an expression in 10th grade) without going through the full distribution process.
Example: (x + 5)² = x² + 2(x)(5) + 5² = x² + 10x + 25
Understanding these concepts and practicing with various examples will help students master the skill of developing algebraic expressions, which is crucial for more advanced mathematical topics.
