Addition and Subtraction of Algebraic Expressions

8.1 Addition and Subtraction of Algebraic Expressions

Description

Quick Overview

This section introduces the principles and methods for adding and subtracting algebraic expressions, highlighting the importance of like terms.

Standard

The section provides a detailed exploration of adding and subtracting algebraic expressions through examples, emphasizing the alignment of like terms. It demonstrates practical methods for performing operations on various expressions, ultimately clarifying the rationale behind algebraic manipulations.

Detailed

Addition and Subtraction of Algebraic Expressions

In this section, we delve into the essentials of adding and subtracting algebraic expressions, which serve as the foundation for algebraic manipulation and solving equations. An algebraic expression consists of variables, constants, and operators. Common examples include expressions like x + 3, 2y - 5, and 3x^2.

Key Concepts

  • Like Terms: Terms that contain the same variables raised to the same power. For instance, in the expression 4xy + 5xy, both terms are like terms because they both contain the variables x and y.
  • Adding Expressions: To add multiple expressions, align like terms vertically to simplify the addition process. For example:
  • Adding 7x^2 - 4x + 5 with 9x - 10 results in:
    7x^2 - 4x + 5
    + 9x - 10
    ---------------
    7x^2 + 5x - 5
  • Subtracting Expressions: Subtraction is equivalent to adding the additive inverse. Students will learn that subtracting a term means adding its opposite. For example, subtracting 5 becomes adding -5.

Significance

Understanding these operations allows students to manipulate algebraic expressions effectively, setting the stage for more complex algebraic concepts, including solving equations and functions.

Key Concepts

  • Like Terms: Terms that contain the same variables raised to the same power. For instance, in the expression 4xy + 5xy, both terms are like terms because they both contain the variables x and y.

  • Adding Expressions: To add multiple expressions, align like terms vertically to simplify the addition process. For example:

  • Adding 7x^2 - 4x + 5 with 9x - 10 results in:

  • 7x^2 - 4x + 5
    • 9x - 10

  • 7x^2 + 5x - 5

  • Subtracting Expressions: Subtraction is equivalent to adding the additive inverse. Students will learn that subtracting a term means adding its opposite. For example, subtracting 5 becomes adding -5.

  • Significance

  • Understanding these operations allows students to manipulate algebraic expressions effectively, setting the stage for more complex algebraic concepts, including solving equations and functions.

Memory Aids

🎵 Rhymes Time

  • Combine like terms, don't be shy, sums will soar high in the sky!

📖 Fascinating Stories

  • When Sandy and other kids (like terms) gather for a pizza dinner (addition), each kid ensures they bring the same amount of the same type of pizza!

🧠 Other Memory Gems

  • Always Keep in Mind (AKM): Align, Keep coefficients, Maintain signs.

🎯 Super Acronyms

A.A.S

  • Align
  • Add/Subtract
  • Simplify.

Examples

  • Example of adding like terms: For the expressions 3x + 4x, the sum is 7x.

  • Example of subtracting: From 5x - 3, if we subtract 2x, we get 3x - 3.

Glossary of Terms

  • Term: Algebraic Expression

    Definition:

    A mathematical statement that contains variables, constants, and operators.

  • Term: Like Terms

    Definition:

    Terms in an expression that have the same variable raised to the same exponent.

  • Term: Coefficient

    Definition:

    A numerical factor in a term of an algebraic expression.

  • Term: Additive Inverse

    Definition:

    The opposite value of a number; it is the value that, when added to the original number, results in zero.