BASIC MATHS FORMULAS
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
The roots for this quadratic equation will be:
Arithmetic Progression
Arithmetic progression
Consider the following arithmetic progression:- a + (a + d) + (a + 2d) + (a + 3d) + ...
- 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:![Sum of the first n term, Sn = n/2[2a + (n-1)d]](data:image/png;base64,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)
Geometric Progression
Geometric progression
Consider the following geometric progression:- a + ar + ar2 + ar3 + ...
- 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:![sum of the first n term, Sn = [a(1-r^n)]/[1-r]](data:image/png;base64,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)
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