Operations with Parentheses and Algebraic Expressions

This page covers important techniques for manipulating algebraic expressions, focusing on operations involving parentheses, expanding, and factoring.

The page begins by explaining the rules for removing parentheses in algebraic expressions:

1. If a parenthesis is preceded by a '+' sign, it can be removed without changing the signs inside.
2. If a parenthesis is preceded by a '-' sign, it can be removed by changing all the signs of the terms inside the parenthesis.

Example: B = 6x - (5x - 8) Solution: B = 6x - 5x + 8 = x + 8

The page then moves on to expanding algebraic expressions, introducing the distributive property:

Definition: k(a + b) = ka + kb and k(a - b) = ka - kb

An example is provided to demonstrate this concept:

A = 3x(2 - 4) - 2(6x + 4) Expanded: A = 6x - 12x - 12x - 8 = -18x - 8

Finally, the page covers factoring algebraic expressions, which is essentially the reverse process of expanding:

Definition: Factoring means finding common factors in an expression and writing it in a more compact form.

Example: A = (2x + 3)(x - 5) + (2x + 3)(3 - 4x) Factored: A = (2x + 3)(x - 5 + 3 - 4x) = (2x + 3)(-3x - 2)

This page provides essential techniques for comment réussir son DM de maths and comment réussir un eval de maths. Understanding these operations is crucial for solving more complex mathematical problems and is often tested in exercices de suppression de parenthèses and exercices de factorisation.

Powers and Exponents

This page introduces the concept of powers and exponents in mathematics, focusing on their properties and applications.

Powers are a way of expressing repeated multiplication, with the base number being multiplied by itself a certain number of times indicated by the exponent. The page provides several examples to illustrate this concept, including special cases like negative exponents and powers of 10.

Definition: A power is expressed as a^n, where 'a' is the base and 'n' is the exponent, representing the n-th power of a.

Example: 2^3 = 2 × 2 × 2 = 8

The page also covers some important properties of powers:

1. Any number raised to the power of 0 equals 1 (e.g., 5^0 = 1)
2. Any number raised to the power of 1 equals itself (e.g., 7^1 = 7)
3. Negative numbers raised to even powers result in positive numbers (e.g., (-6)^2 = 36)
4. Negative numbers raised to odd powers remain negative (e.g., (-3)^3 = -27)

Highlight: Powers of 10 are given special attention due to their importance in scientific notation and calculations.

The page concludes with some problem-solving examples involving powers, demonstrating how to apply the concepts in practice.

Example: A = 7^2 + (-2)^5 × 6 Solution: A = 49 + (-32) × 6 = 49 + (-192) = -143

This comprehensive introduction to powers and exponents provides a solid foundation for students learning about écriture scientifique and preparing for évaluations de maths.