Prove: `|(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a b,-a b)|=(a b+b c+c a)^3`

Explanation

`Delta=|(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a b,-a b)|`


Multiplying `underset(1)(R),underset(2)(R)` and `underset(3)(R)` with `a`,`b` and `c`


`implies frac{1}{abc}|(-abc, ab^2+abc,ac^2+abc), (a^2b+ab c,-a bc,bc^2+a bc),( a^2c+a bc,cb^2+a bc,-a bc)|`


Divide `underset(1)(C)underset(2)(C)underset(3)(C)` with `a,b` and `c`


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