Extended Distributive Law

The extended distributive law is a fundamental principle in algebra that allows for the simplification of complex expressions. This law expands on the basic distributive property, enabling students to handle more intricate mathematical problems with greater ease.

Definition: The extended distributive law states that when multiplying a sum by another sum, each term of one factor is multiplied by each term of the other factor, and the results are then added together.

The page demonstrates this concept through a detailed example:

(a + b) · (c + d) = ac + ad + bc + bd

This equation illustrates how the law works in practice, showing that each term in the first bracket (a and b) is multiplied by each term in the second bracket (c and d), resulting in four separate products that are then summed.

Example: The problem (3 - a) · (5 + b) is solved step-by-step, demonstrating the application of the extended distributive law:

1. 3 · 5 + 3 · b - a · 5 - a · b
2. 15 + 3b - 5a - ab

Highlight: This method of expanding brackets is essential for simplifying and solving more complex algebraic equations, making it a crucial skill for students to master in algebra and higher mathematics.

The page also touches on the importance of understanding this concept for tackling more advanced mathematical problems, emphasizing its relevance in distributivgesetz 5. klasse and beyond.

Vocabulary: Terms like "factor" and "product" are essential in understanding the distributive law. A factor is a number or expression that is multiplied, while a product is the result of multiplication.

By mastering the extended distributive law, students gain a powerful tool for simplifying and solving a wide range of algebraic expressions, setting a strong foundation for more advanced mathematical concepts.