# Basic Algebra/Solving Equations/Formulas

### Basic Formulas

1. ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$
2. ${\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}}$
3. ${\displaystyle a^{2}-b^{2}=(a+b)(a-b)}$
4. ${\displaystyle (a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}}$
5. ${\displaystyle (a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}}$
6. ${\displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})}$
7. ${\displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})}$
8. ${\displaystyle (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}$
9. ${\displaystyle a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)}$

### Derivation (1)

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