*Some Basic Formulae:*

- (
*a*+*b*)(*a*–*b*) = (*a*^{2}–*b*^{2}) - (
*a*+*b*)^{2}= (*a*^{2}+ b^{2}+ 2*ab*) - (
*a*–*b*)^{2}= (*a*^{2}+ b^{2}– 2*ab*) - (
*a*+*b*+*c*)^{2}=*a*^{2}+ b^{2}+*c*^{2}+ 2(*ab*+*bc*+*ca*) - (
*a*^{3}+*b*^{3}) = (*a*+*b*)(*a*^{2}–*ab*+*b*^{2}) - (
*a*^{3}–*b*^{3}) = (*a*–*b*)(*a*^{2}+*ab*+*b*^{2}) - (
*a*^{3}+*b*^{3}+*c*^{3}– 3*abc*) = (*a*+*b*+*c*)(*a*^{2}+*b*^{2}+*c*^{2}–*ab*–*bc*–*ac*) - When
*a*+*b*+*c*= 0, then*a*^{3}+*b*^{3}+*c*^{3}= 3*abc*.