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Question

Find the product
(2a+b+c)(4a2+b2+c22abbc2ca)

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Solution

By using the identity

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

(2a+b+c)(4a2+b2+c22abbc2ca)
=8a3+b3+c34a22ab2ab22abcb2cbc22a2c2abc2ac2+4a2b+4a2c+2ab2+b2c+2ac2+bc2
=8a3+b3+c36abc

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