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
- a^{2} - b^{2} = (a-b)(a+b)
Difference of Cubes
- a^{3} - b^{3} = (a - b)(a^{2}+ ab + b^{2})
Sum of Cubes
- a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})
Special Algebra Expansions
Formula for (a+b)^{2} and (a-b)^{2}
- (a + b)^{2} = a^{2} + 2ab + b^{2}
- (a - b)^{2} = a^{2} - 2ab +b^{2}
Formula for (a+b)^{3} and (a-b)^{3}
- (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
- (a - b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}
Roots of Quadratic Equation
Formula
Consider this quadratic equation:
- ax^{2} + bx + c = 0
Where a, b 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 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
Geometric progression
Consider the following geometric progression:
- a + ar + ar^{2} + ar^{3} + ...
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: