# Algebraic Identities | Algebraic Formulas

The following are some basic Algebraic Identities or Algebraic Formulas:

## Algebraic Identity 1

$\displaystyle {{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$

### Algebraic Identity 2

$\displaystyle {{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$

### Algebraic Identity 3

$\displaystyle {{(a+b+c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2ab+2bc+2ca$

### Algebraic Identity 4

$\displaystyle (x+a)(x-b)=x+(a=b)x+ab$

### Algebraic Identity 5

$\displaystyle {{(a-b)}^{3}}={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}$

### Algebraic Identity 6

$\displaystyle {{(a+b)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}$

### Algebraic Identity 7

$\displaystyle {{(a-b)}^{4}}={{a}^{4}}-4{{a}^{3}}b+6{{a}^{2}}{{b}^{2}}-4a{{b}^{3}}+{{b}^{4}}$

### Algebraic Identity 8

$\displaystyle {{(a+b)}^{4}}={{a}^{4}}+4{{a}^{3}}b+6{{a}^{2}}{{b}^{2}}+4a{{b}^{3}}+{{b}^{4}}$

### Algebraic Identity 9

$\displaystyle {{a}^{2}}-{{b}^{2}}=(a+b)(a-b)$

### Algebraic Identity 10

$\displaystyle {{a}^{2}}+{{b}^{2}}={{(a+b)}^{2}}-2ab$

### Algebraic Identity 11

$\displaystyle {{a}^{3}}-{{b}^{3}}=(a-b)({{a}^{2}}+ab+{{b}^{2}})$

### Algebraic Identity 12

$\displaystyle {{a}^{3}}+{{b}^{3}}=(a+b)({{a}^{2}}-ab+{{b}^{2}})$

### Algebraic Identity 13

$\displaystyle {{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=(a+b+c)({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca)$

### Algebraic Identity 14

$\displaystyle {{a}^{4}}-{{b}^{4}}=({{a}^{2}}-{{b}^{2}})({{a}^{2}}+{{b}^{2}})=(a+b)(a-b)({{a}^{2}}+{{b}^{2}})$

### Algebraic Identity 15

$\displaystyle {{a}^{5}}-{{b}^{5}}=(a-b)({{a}^{4}}+{{a}^{3}}b+{{a}^{2}}{{b}^{2}}+a{{b}^{3}}+{{b}^{4}})$

### Algebraic Identity 16

$\displaystyle {{a}^{5}}+{{b}^{5}}=(a+b)({{a}^{4}}-{{a}^{3}}b+{{a}^{2}}{{b}^{2}}-a{{b}^{3}}+{{b}^{4}})$