a³ + b³ + c³ - 3abc এর সূত্র কোনটি?

a³ + b³ + c³ - 3abc = (a + b + c)( a² + b² + c² - ab - bc - ca)
প্রমাণ:
a³ + b³ + c³ - 3abc
= (a + b)³ - 3ab(a + b) + c3 - 3abc
= (a³ + b³) + c³ - 3ab(a + b) - 3abc
= (a + b + c){(a + b)² - (a + b)c + c²)- 3ab(a + b + c)
= (a + b + c){(a² +2ab + b² - ac - bc + c²)- 3ab(a + b + c)
= (a + b + c){(a² +2ab + b² - ac - bc + c²)- 3ab}
= (a + b + c)(a² + b² + c² - ab - bc - ca)