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Question

Evaluate a3+b3+c33abc(a+b+c),where(a+b+c)0.


A
a2+b2+c2abbcca
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B
a2+b2+c2+abbcca
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C
a2+b2+c2+ab+bc+ca
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D
a2b2c2+ab+bc+ca
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Solution

The correct option is A a2+b2+c2abbcca

We have the identity
a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)

Taking (a+b+c) from R.H.S. to L.H.S., we get

a3+b3+c33abc(a+b+c)=a2+b2+c2abbcca


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