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Basic Important Formulas

These are the basic formulae:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

(a + b)² - (a - b)² = 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a² - b²) = (a + b)(a - b)

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

(a³ + b³) = (a + b)(a² - ab + b²)

(a³ - b³) = (a - b)(a² + ab + b²)

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

If a + b + c = 0 then a³ + b³ + c³ = 3abc