Prove: `|[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3`

Explanation

`Delta = |{:(b+c,,a-b,,a),(c+a,,b-c,,b),(a+b,,c-a,,c):}|`
`=|{:(b+c,,-b,,a),(c+a,,-c,,b),(a+b,,-a,,c):}|" ""[Applying "C_(2) toC_(2)-C_(3)"]"`
`=|{:(c,,-b,,a),(a,,-c,,b),(b,,-a,,c):}|" ""[Applying "C_(1) toC_(1)+C_(2)"]"`
`=|{:(c,,a,,b),(a,,b,,c),(b,,c,,a):}|" ""[Interchanging " C_(2) " and "C_(3)"]"`
`=3abc -a^(3)-b^(3)-c^(3)`