Page 2: Double Distributivity

This page focuses on the concept of double distributivity, an advanced technique in Calcul littéral 3ème Développer et réduire. It's a crucial skill for simplifying more complex algebraic expressions.

Definition: Double distributivity is the process of multiplying two binomials a+b$$c+d, resulting in ac + ad + bc + bd.

Example: $6 + 4$ × $2 + 3$

1. Distribute the first term: 6 × 2 + 6 × 3
2. Distribute the second term: 4 × 2 + 4 × 3
3. Combine: 12 + 18 + 8 + 12 = 50

Example: 6 - 4$$2 + 3

1. Rewrite as 6 + (-4)$$2 + 3
2. Distribute: 6 × 2 + 6 × 3 + $-4$ × 2 + $-4$ × 3
3. Simplify: 12 + 18 - 8 - 12 = 10

Example: 5 - 7x$$3x - 9

1. Rewrite as 5 + (-7x)$$3x + (-9)
2. Distribute: 5 × 3x + 5 × $-9$ + $-7x$ × 3x + $-7x$ × $-9$
3. Simplify: 15x - 45 - 21x² + 63x
4. Combine like terms: -21x² + 78x - 45

These examples demonstrate the application of double distributivity in various scenarios, showcasing its importance in Exercice Développement Factorisation avec corrigé pdf.

Page 1: Developing, Reducing, and Factoring Expressions

This page covers essential algebraic operations including developing and reducing expressions, factoring, and solving equations. These are fundamental skills for Calcul littéral 3ème Développer et réduire.

Example: To develop and reduce $4y-3$ × 2 + y:

1. Distribute: 4y × 2 - 3 × 2 + y
2. Simplify: 8y - 6 + y
3. Combine like terms: 9y - 6

Example: Factoring 21x + 6y: Factor out the greatest common factor: 3$7x + 2y$

Highlight: Solving equations is a crucial skill in Exercice Calcul littéral 3ème TYPE brevet. The page demonstrates various equation-solving techniques:

1. -2y + 5 = -12 Solve by isolating the variable: -2y = -17 y = 8.5

2. -17x + 7 = -42 Solve by isolating the variable: -17x = -49 x = 2.88

3. 5x$7-2x$ = 120 Expand the expression: 35x - 10x² = 120 Rearrange to standard form: 10x² - 35x + 120 = 0 Solve using the quadratic formula or factoring

These examples showcase the application of Développer et réduire exercice corrigé techniques in various algebraic contexts.