Basic Algebra Formulas

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Introduction
This page contains basic algebra formulas that are most commonly used. These formulas are categorized below:
  1. Algebra Identities
  2. Special Algebra Expansions
  3. Roots of Quadratic Equation
  4. Arithmetic Progression
  5. Geometric Progression
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Algebra Identities

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Difference of squares
difference of squares
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Difference of cubes
difference of cubes
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Sum of cubes
sum of cubes

Special Algebra Expansions

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 Formula for (a+b)2 and (a-b)2
Expanded (a+b)^2
Expanded (a-b)^2
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 Formula for (a+b)3 and (a-b)3
Expanded (a+b)^3
Expanded (a-b)^3

Roots of Quadratic Equation

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Formula
Consider this quadratic equation: 
quadratic equation: ax^2 +bx +c = 0

Where a, b and c are the leading coefficients.

The roots for this quadratic equation will be:
roots of quadratic equation

Arithmetic Progression

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Arithmetic progression
Consider the following arithmetic progression:
arithmetic progression: a+(a+d)+(a+2d)+(a+3d)+...

Where:
  1. a is the initial term
  2. d is the common difference
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The nth term
The nth term, Tn of the arithmetic progression is:
The n term, Tn = a+(n-1)d


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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]


Geometric Progression

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Geometric progression
Consider the following geometric progression:
geometric progression, a + ar + ar^2 + ar^3 +...

Where:
  1. a is the scale factor
  2. r is the common ratio
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The nth term
The nth term, Tn of the geometric progression is:
nth term, Tn=ar^(n-1)


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The 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]

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The sum to infinity
If -1 < r < 1, the sum to infinity, S is:
Sum to infinity, a/(1-r)

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