Developing Literal Expressions
This page focuses on developing literal expressions, which is the inverse process of factorization.
Simple Development
Definition: Developing a literal expression means transforming a product into a sum or difference.
The general forms for simple development are:
Ka+b = K × a + K × b = Ka + Kb
Ka−b = K × a - K × b = Ka - Kb
Where K, a, and b are numbers.
Example: 3x+2 = 3 × x + 3 × 2 = 3x + 6
Several examples are provided to illustrate this concept:
- 55−x = 5 × 5 - 5 × x = 25 - 5x
- xx+4 = x × x + x × 4 = x² + 4x
- 3x4−2 = 3x × 4 - 3x × 2 = 12x - 6x
Double Development
The page also introduces the concept of double development, which involves multiplying two binomials.
Highlight: The general form for double development is:
a+bc+d = a × c + a × d + b × c + b × d = ac + ad + bc + bd
Where a, b, c, and d are numbers.
This formula is crucial for développer et réduire exercices corrigés and is often featured in calcul littéral 3ème exercices corrigés.
Vocabulary: Binomial - An algebraic expression consisting of two terms.
Understanding these concepts of developing literal expressions is essential for mastering calcul littéral 3ème and preparing for more advanced algebraic manipulations in higher grades.