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Basic formula for Algebra

Basic Algebra Formulas

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
Algebra Identities

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)
Special Algebra Expansions

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
Roots of Quadratic Equation

Formula

Consider this quadratic equation:

  • ax2 + bx + c = 0

Where ab and c are the leading coefficients.

The roots for this quadratic equation will be:

  •  
Arithmetic Progression

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 nth term

The nth term, Tn of the arithmetic progression is:

  • Tn = a + (n – 1)d

Sum of the first n term

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

  •  
Geometric Progression

Geometric progression

Consider the following geometric progression:

  • a + ar + ar2 + ar3 + …

Where:

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

The nth term

The nth term, Tn of the geometric progression is:

  • Tn = ar n – 1

Sum of the first n terms

The sum of the first n terms, Sn is:

  •  

The sum to infinity

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