Basics of Algebra

Algebra is a fundamental branch of mathematics that uses symbols, typically letters, to represent unknown values called variables. Known values are called constants. Algebra combines variables and constants using basic operations like addition, subtraction, multiplication, and division to form expressions and equations.

For example, in the equation x + 10 = 0, x is the unknown value to be solved. Algebra is essential across many areas of mathematics, including calculus, geometry, and trigonometry, providing tools to model and solve real-world problems.

Algebra Rules

There are five basic rules of algebra, including:

• Commutative Rule of Addition
• Commutative Rule of Multiplication
• Associative Rule of Addition
• Associative Rule of Multiplication
• Distributive Rule of Multiplication

These rules are explained in the image below:

Algebraic Operations

The four basic algebraic operations are:

• Addition: (a + b)
• Subtraction: (a - b)
• Multiplication: (a × b)
• Division: (a ÷ b)

The operations follow the BODMAS rule, which is:

Brackets → Orders (Exponents and Roots) → Division → Multiplication → Addition → Subtraction.

Important Formulas

Given below are some important algebraic formulas which will help in quick calculation: