Algebra — Complete Study Guide
Introduction to Algebra
1. What is Algebra?
Algebra is a branch of mathematics where we use letters or symbols (variables) to represent
unknown numbers.
It allows us to solve problems systematically and understand mathematical relationships.
Example:
x + 5 = 12
Solve for x → x = 7
Why Algebra?
Simplifies complex arithmetic problems
Helps in solving equations
Essential for higher mathematics, science, engineering
2. Key Terms in Algebra
Term Definition Example
Variable Symbol representing unknown value x, y, z
Constant Fixed number 2, 5, 10
Coefficient Number multiplying a variable 3x → 3
Expression Combination of variables & constants 2x + 5
Equation Statement that two expressions are equal 2x + 3 = 11
, Types of Equations & Operations
1. Types of Equations
1. Linear Equation: Highest power of variable = 1
Example: 2x + 3 = 11
2. Quadratic Equation: Highest power = 2
Example: x² – 5x + 6 = 0
3. Cubic Equation: Highest power = 3
Example: x³ – 3x² + 2x = 0
4. Inequalities: Equations with <, >, ≤, ≥
Example: 3x + 2 > 8
2. Basic Algebraic Operations
Addition/Subtraction: (x + 3) + (x – 2) = 2x + 1
Multiplication: 2x × 3x = 6x²
Division: (6x² ÷ 2x) = 3x
Expanding: (x + 2)(x + 3) = x² + 5x + 6
Introduction to Algebra
1. What is Algebra?
Algebra is a branch of mathematics where we use letters or symbols (variables) to represent
unknown numbers.
It allows us to solve problems systematically and understand mathematical relationships.
Example:
x + 5 = 12
Solve for x → x = 7
Why Algebra?
Simplifies complex arithmetic problems
Helps in solving equations
Essential for higher mathematics, science, engineering
2. Key Terms in Algebra
Term Definition Example
Variable Symbol representing unknown value x, y, z
Constant Fixed number 2, 5, 10
Coefficient Number multiplying a variable 3x → 3
Expression Combination of variables & constants 2x + 5
Equation Statement that two expressions are equal 2x + 3 = 11
, Types of Equations & Operations
1. Types of Equations
1. Linear Equation: Highest power of variable = 1
Example: 2x + 3 = 11
2. Quadratic Equation: Highest power = 2
Example: x² – 5x + 6 = 0
3. Cubic Equation: Highest power = 3
Example: x³ – 3x² + 2x = 0
4. Inequalities: Equations with <, >, ≤, ≥
Example: 3x + 2 > 8
2. Basic Algebraic Operations
Addition/Subtraction: (x + 3) + (x – 2) = 2x + 1
Multiplication: 2x × 3x = 6x²
Division: (6x² ÷ 2x) = 3x
Expanding: (x + 2)(x + 3) = x² + 5x + 6
