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Doubt & Answer Explanation

Doubt

prove that
determinant            b2+c2      ab          ac
                             ab         c2+a2       bc           = 4a2b2c2
                             ca            cb       a2+b2    

Answer Explanation

D = (b2 + c2) [(c2 + a2)*(a2 + b2) - b2c2] - (ab)[ab*(a2 + b2) - bc*ca] + ac[ab*cb - ca*(c2 + a2)]
= (b2 + c2)[a4 +a2c2 +a2b2 + b2c2 - b2c2] - (ab)[a3b + ab3 -abc2] + (ac)[ab2c - ac3 -a3c]
= a4b2 + a4c2 + a2b2c2 + a2c4 + a2b4 + a2b2c2 - a4b2 - a2b4 + a2b2c2 + a2b2c2 - a2c4 - a4c2
 = 4a2b2c2

Note: Atleast try some questions. you are in habit of asking question without trying. I am sorry Ibut you will not be answered if you will repeat this habit. Its for your own good. Try to solve questions.

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