a\(^3\)-b\(^3\)+c\(^{^{ }3}\)+3abc
=a\(^3\)-b\(^3\)+c\(^3\)+3abc+3a\(^2\)b+3ab\(^2\)-3a\(^2\)b-3ab\(^2\)
=(a-b)\(^3\)+c\(^3\)+3ab(a-b+c)
=(a-b+c)[(a-b)\(^2\)-(a-b)c+c\(^2\)]+3ab(a-b+c)
=(a-b+c)(a\(^2\)+b\(^2\)+c\(^2\)-ab-ac+bc)
a33-b33+c33+3abc
=a33-b33+c33+3abc+3a22b+3ab22-3a22b-3ab22
=(a-b)33+c33+3ab(a-b+c)
=(a-b+c)[(a-b)22-(a-b)c+c22]+3ab(a-b+c)
=(a-b+c)(a22+b22+c22-ab-ac+bc)