항등식

항등식

( a ± b )² = a² ± 2ab + b²
( a ± b )³ = a³ ± 3a²b + 3ab² ± b³
( a ± b )⁴ = a⁴ ± 4a³b + 6a²b² ± 4ab³ + b⁴
( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca
( a + b - c )² = a² + b² + c² + 2ab - 2bc - 2ca
( a - b - c )² = a² + b² + c² - 2ab - 2bc + 2ca

a² - b² = ( a - b )( a + b )
a³ + b³ = ( a + b )( a² - ab + b² )
a³ - b³ = ( a - b )( a² + ab + b² )

a⁵ + b⁵ = ( a + b )( a⁴ - a³b + a²b² - ab³ + b⁴ )
a⁵ - b⁵ = ( a - b )( a⁴ + a³b + a²b² + ab³ + b⁴ )