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Question

If D=∣ ∣ ∣a2+1abacbab2+1bccacbc2+1∣ ∣ ∣ then D=

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Solution

D=∣ ∣ ∣a2+1abacbab2+1bccacbc2+1∣ ∣ ∣
=(a2+1)(b2c2+b2+c2+1b2c2)ab(abc2+ababc2)+ac(ab2cab2cac)
=(a2+1)(b2+c2+1)ab(ab)+ac(ac)
=a2b2+a2c2+a2+b2+c2+1a2b2a2c2
=a2+b2+c2+1

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