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
