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Basic Algebra Formulas

Introduction

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

• Algebra Identities

• Special Algebra Expansions

• Roots of uadratic E!uation

• Arithmetic "rogression

• #eometric "rogression

Algebra Identities

Difference of Squares

•

a$

  % b$

  & 'a%b('a)b(

Difference of Cubes

• a*  % b*  & 'a % b('a$ ) ab ) b$ (

Sum of Cubes

• a*  ) b*  & 'a ) b('a$  % ab ) b$ (

Special Algebra Expansions

Formula for (a+b)  and (a!b) 

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• 'a ) b($  & a$  ) $ab ) b$ 

• 'a % b($  & a$  % $ab )b$ 

Formula for (a+b)"  and (a!b)" 

• 'a ) b(*  & a*  ) *a$ b ) *ab$  ) b* 

• 'a % b(*  & a*  % *a$ b ) *ab$  % b* 

#oots of $uadratic Equation

Formula

+onsider this !uadratic e!uation:

• ax$  ) bx ) c & ,

-here a b and c are the leading coefficients.

The roots for this !uadratic e!uation will be:

•

Arit%metic &rogression

Arit%metic progression

+onsider the following arithmetic progression:

• a ) 'a ) d( ) 'a ) $d( ) 'a ) *d( ) ...

-here:

• a is the initial term

• d is the common difference

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'%e nt%  term

The nth  term Tn of the arithmetic progression is:

• Tn & a ) 'n % /(d

Sum of t%e first n term

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

•

eometric &rogression

eometric progression

+onsider the following geometric progression:

• a ) ar ) ar $  ) ar *  ) ...

-here:

• a is the scale factor 

• r is the common ratio

'%e nt%  term

The nth  term Tn of the geometric progression is:

• Tn & ar n % / 

Sum of t%e first n terms

The sum of the first n terms Sn is:

•

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'%e sum to infinit

If %/ 0 r 0 / the sum to infinity S1 is:

•