Advanced Factorization Techniques

This page delves deeper into factorization techniques, building upon the distributivity concepts introduced earlier. It provides more complex examples and exercises to challenge students' understanding.

Vocabulary: Factorization is the process of breaking down an algebraic expression into a product of simpler expressions.

The page starts by presenting factorization rules:

• ka + kb = k(a + b)
• ka - kb = k(a - b)

Example: 2x - 14 can be factored as 2(x - 7)

Several more examples are provided to illustrate different factorization scenarios:

• 3y - 5y = y(3 - 5) = -2y
• 75ab - 25a + 15ac = 5a(15b - 5 + 3c)
• 3x + 6xy = 3x(1 + 2y)

The page then moves on to more complex exercises, demonstrating how to factor and simplify intricate expressions:

Example: A = (x - 3)(2x + 5) - (x - 3)(x - 7) Solution: A = (x - 3)[(2x + 5) - (x - 7)] = (x - 3)(3x - 2)

Another complex example is provided:

B = (2x + 3)(x + 8) - (3x - 2)(2x + 3)

The solution process is shown step-by-step, culminating in the final factored form:

B = 2(2x + 3)(x + 5)

Highlight: These complex exercises are excellent practice for développement et factorisation exercices corrigés PDF 4ème and factorisation 3ème exercice corrigé, helping students master advanced algebraic manipulation techniques.

Distributivity: Developing and Factoring Expressions

This page introduces the concept of distributivity in algebra, focusing on developing and factoring expressions. It covers both simple and double distributivity, providing clear examples and rules for students to follow.

Definition: Distributivity is a fundamental property in algebra that allows us to multiply a number or variable by a sum or difference.

The page outlines two main types of distributivity:

1. Simple Distributivity: k(a + b) = ka + kb
2. Double Distributivity: (a + b)(c + d) = ac + ad + bc + bd

Example: For simple distributivity, 13 × 101 can be calculated as 13 × (100 + 1) = 1300 + 13 = 1313.

The page also covers reducing and factoring expressions, providing a formula for expanding the product of two binomials:

(a + b)(c + d) = ac + ad + bc + bd (a + b)(c - d) = ac - ad + bc - bd

Highlight: These formulas are crucial for solving more complex algebraic problems and are essential for students to memorize.

The page concludes with an equation to solve: 3(x - 1) = 5(x + 1) + x, demonstrating how to apply distributivity in problem-solving.