Some Basic Formulae:

1. (a + b)(a - b) = (a² - b²)

2. (a + b)² = (a² + b² + 2ab)

3. (a - b)² = (a² + b² - 2ab)

4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

5. (a³ + b³) = (a + b)(a² - ab + b²)

6. (a³ - b³) = (a - b)(a² + ab + b²)

7. (a³ + b³ + c³ - 3abc) = (a + b + c)(a² + b² + c² - ab - bc - ac)

8. When a + b + c = 0, then a³ + b³ + c³ = 3abc.