Introduction

This page contains basic algebra formulas that are most commonly used. These formulas are categorized below:

• Algebra Identities
• Special Algebra Expansions
• Roots of Quadratic Equation
• Arithmetic Progression
• Geometric Progression

Difference of Squares

• a² - b² = (a-b)(a+b)

Difference of Cubes

• a³ - b³ = (a - b)(a²+ ab + b²)

Sum of Cubes

• a³ + b³ = (a + b)(a² - ab + b²)

Formula for (a+b)² and (a-b)²

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab +b²

Formula for (a+b)³ and (a-b)³

• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a - b)³ = a³ - 3a²b + 3ab² - b³

Formula

Consider this quadratic equation:

• ax² + bx + c = 0

Where a, b and c are the leading coefficients.

The roots for this quadratic equation will be:

• 

Arithmetic progression

Consider the following arithmetic progression:

• a + (a + d) + (a + 2d) + (a + 3d) + ...

Where:

• a is the initial term
• d is the common difference

The n^th term

The n^th term, T_n of the arithmetic progression is:

• T_n = a + (n - 1)d

Sum of the first n term

The sum of the first n terms of the arithmetic progression is:

• 

Geometric progression

Consider the following geometric progression:

• a + ar + ar² + ar³ + ...

Where:

• a is the scale factor
• r is the common ratio

The n^th term

The n^th term, T_n of the geometric progression is:

• T_n = ar ^{n - 1}

Sum of the first n terms

The sum of the first n terms, S_n is:

• 

The sum to infinity

If -1 < r < 1, the sum to infinity, S_∞ is:

•