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Question

prove that a3(bc)3+b3(ca)3+c3(ab)3= a3(cb)+b3(ac)+c3(ba)

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Solution

We have,


a(bc)3+b(ca)3+c(ab)3

a(b3c33bc(bc))+b(c3a33ac(ca))+c(a3b33ab(ab))

a(b3c33b2c+3bc2)+b(c3a33ac2+3a2c)+c(a3b33a2b+3ab2)

ab3ac33ab2c+3abc2+bc3ba33abc2+3a2bc+ca3cb33a2bc+3ab2c

ab3ac3+bc3ba3+ca3cb3

a3(cb)+b3(ac)+c3(ba)

Hence proved.

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