Multiplication and Division of Algebraic Expressions

This page provides a detailed explanation of mnożenie i dzielenie wyrażeń algebraicznych by numbers. It covers various examples and rules for performing these operations correctly.

Definition: Algebraic expressions are mathematical phrases that combine numbers, variables, and operations to represent a value or relationship.

The page is divided into two main sections: multiplication and division.

Multiplication of Algebraic Expressions

The document begins with examples of multiplying algebraic expressions by numbers. It demonstrates how to multiply single terms, binomials, and trinomials by constants.

Example: 2·a = 2a, showing that multiplying a variable by a number results in the coefficient being applied to the variable.

Highlight: When multiplying a negative number by an algebraic expression, the signs of all terms in the expression change.

Some more complex examples are provided, such as:

• $2x² + 4 + 2y$ · (-3) = -6x² - 12 - 6y
• 3 · $-2a + 5 - 2b$ = -6a + 15 - 6b

These examples illustrate the distributive property of multiplication over addition in algebraic expressions.

Division of Algebraic Expressions

The second part of the page focuses on dividing algebraic expressions by numbers. It shows how to simplify expressions by dividing each term by the given number.

Example: 6a ÷ 2 = 3a, demonstrating that when dividing an algebraic term by a number, we divide the coefficient while keeping the variable unchanged.

More examples include:

• -10b ÷ 5 = -2b
• 15c ÷ 3 = 5c
• $6a + 2b + 4c$ ÷ 2 = 3a + b + 2c

Vocabulary: Coefficient - the numerical factor in an algebraic term, such as 6 in 6x².

This comprehensive overview provides students with a solid foundation for understanding mnożenie i dzielenie wyrażeń algebraicznych, which is crucial for more advanced algebraic operations and problem-solving in mathematics.