Basic Algebra Formulas

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Introduction

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

Algebra Identities

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Difference of Squares

  • a2 - b2 = (a-b)(a+b)
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Difference of Cubes

  • a3 - b3 = (a - b)(a2+ ab + b2)
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Sum of Cubes

  • a3 + b3 = (a + b)(a2 - ab + b2)

Special Algebra Expansions

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Formula for (a+b)2 and (a-b)2

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

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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:

  • roots of quadratic equation

Arithmetic Progression

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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
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The nth term

The nth term, Tn of the arithmetic progression is:

  • 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:

  • a + ar + ar2 + ar3 + ...

Where:

  • a is the scale factor
  • r is the common ratio
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The nth term

The nth term, Tn of the geometric progression is:

  • Tn = ar n - 1
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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)