Prove that the following determinant is equal to (ab + bc + ca)3 :

-bc b2 + bc c2 + bc

a2 + ac -ac c2 + ac

a2 + ab b2 + ab -ab

1) multiply R1,R2,R3 with a,b,c respectively.

2) divide a,b,c from C1,C2,C3 respectively.

3) R1:R1+R2+R3.

4) after applying take (ab+bc+ac) from R1.

5) C1:C1-C3 , C2;C2-C3. 

6) after applying take (ab+bc+ac) common from C1 and C2 both .

7) the expand the remaining determinant w.r.t R1.

     HENCE PROVE   

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Answer for Vishal 
195*205 = (200-5)(200+5)
              = (200)^2-(5)^2
              = 40000-25
              = 39975
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