Page 2: Advanced Algebraic Operations and Notable Identities

This page delves deeper into Développer et réduire une expression en ligne, focusing on more complex expansions and the third remarkable identity.

The page starts with a detailed example of expanding and reducing: (2x + 3)(x + 5) = 2x² + 10x + 3x + 15 = 2x² + 13x + 15 (7x + 6)(2x - 1) = 14x² - 7x + 12x - 6 = 14x² + 5x - 6

Example: When expanding (2x + 3)(x + 5), we multiply each term of the first bracket by each term of the second: 2x × x, 2x × 5, 3 × x, and 3 × 5.

The page then introduces the third remarkable identity: (a + b)(a - b) = a² - b²

Highlight: The third remarkable identity is crucial for simplifying certain types of expressions quickly.

Examples of applying this identity are provided: (5x + 6)(5x - 6) = (5x)² - 6² = 25x² - 36 (9x + 3)(9x - 3) = (9x)² - 3² = 81x² - 9

Vocabulary: A remarkable identity is a standard algebraic formula that can be applied to simplify expressions quickly.

The page concludes with an example of factoring using the third remarkable identity: 36x² - 16 = (6x)² - 4² = (6x + 4)(6x - 4)

Definition: Factoring using the third remarkable identity involves recognizing the pattern a² - b² and rewriting it as (a + b)(a - b).

This comprehensive guide provides students with a solid foundation in algebraic operations, preparing them for more advanced mathematical concepts.