Algebra Basics

Algebra

What is Algebra?

• A branch of mathematics that deals with variables and their relationships
• Involves the study of algebraic expressions, equations, and functions

Key Concepts

• Variables: Letters or symbols that represent unknown values or quantities
• Constants: Numbers that do not change value
• Algebraic Expressions: Combinations of variables, constants, and mathematical operations
• Equations: Statements that express the equality of two algebraic expressions
• Functions: Relations between a set of inputs (domain) and a set of possible outputs (range)

Types of Algebraic Expressions

• Monomials: Expressions with a single term (e.g. 2x, 3y)
• Binomials: Expressions with two terms (e.g. x + 3, 2x - 4)
• Polynomials: Expressions with multiple terms and variables (e.g. x^2 + 3x - 4, 2y^2 - 5y + 1)

Operations on Algebraic Expressions

• Addition and Subtraction: Combining like terms
• Multiplication: Distributive property (e.g. 2(x + 3) = 2x + 6)
• Division: Factoring and canceling out common terms

Solving Equations

• Linear Equations: Equations with a degree of 1 (e.g. 2x + 3 = 5)
• Quadratic Equations: Equations with a degree of 2 (e.g. x^2 + 4x + 4 = 0)
• Systems of Equations: Sets of equations with multiple variables

Graphing and Functions

• Graphs: Visual representations of functions on a coordinate plane
• Domain and Range: The set of inputs and possible outputs of a function
• Function Operations: Composition, inverse, and identity functions

Algebra

Definition and Scope

• Algebra is a branch of mathematics that deals with variables and their relationships
• It involves the study of algebraic expressions, equations, and functions

Key Concepts

Variables and Constants

• Variables are letters or symbols that represent unknown values or quantities
• Constants are numbers that do not change value

Algebraic Expressions

• Algebraic expressions are combinations of variables, constants, and mathematical operations

Equations

• Equations are statements that express the equality of two algebraic expressions

Functions

• Functions are relations between a set of inputs (domain) and a set of possible outputs (range)

Types of Algebraic Expressions

Monomials

• Monomials are expressions with a single term (e.g. 2x, 3y)

Binomials

• Binomials are expressions with two terms (e.g.x + 3, 2x - 4)

Polynomials

• Polynomials are expressions with multiple terms and variables (e.g.x^2 + 3x - 4, 2y^2 - 5y + 1)

Operations on Algebraic Expressions

Addition and Subtraction

• Combine like terms to add or subtract algebraic expressions

Multiplication

• Use the distributive property to multiply algebraic expressions (e.g. 2(x + 3) = 2x + 6)

Division

• Factor and cancel out common terms to divide algebraic expressions

Solving Equations

Linear Equations

• Linear equations have a degree of 1 (e.g. 2x + 3 = 5)

Quadratic Equations

• Quadratic equations have a degree of 2 (e.g.x^2 + 4x + 4 = 0)

Systems of Equations

• Systems of equations involve sets of equations with multiple variables

Graphing and Functions

Graphs

• Graphs are visual representations of functions on a coordinate plane

Domain and Range

• Domain is the set of inputs of a function
• Range is the set of possible outputs of a function

Function Operations

• Composition, inverse, and identity functions are types of function operations

Learn the fundamentals of algebra, including variables, constants, algebraic expressions, and equations. Understand the core concepts of this branch of mathematics.