Using properties of determinants prove
|b+c a a |
| b c+a b |=4abc
| c c a+b |

Dear student  Let  = b+caabc+abcca+bApplying R1 = R1 + R2 + R3, we get = 2b+c2c+a2a+bbc+abcca+b = 2b+cc+aa+bbc+abcca+bApplying R2 = R2 - R1 and R3 = R3 - R1, we get = 2b+cc+aa+b-c0-a-b-a0Apply R1 = R1 + R2 + R3, we get = 20cb-c0-a-b-a0=2-c0-ab + bac-0=2abc+abc=22abc=4abc

Regards    

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