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}})