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Question
Evaluate: (a2 + b2 + c2 - ab - bc - ca)(a + b + c)
Solution
(a2 + b2 + c2 - ab - bc - ca)(a + b + c)
= a (a2 + b2 + c2 - ab - bc - ca) + b (a2 + b2 + c2 - ab - bc - ca) + c (a2 + b2 + c2 - ab - bc - ca)
= a3 + ab2 + ac2 - a2b - abc - ca2 +a2b + b3 + bc2 - ab2 - b2c - abc + a2c + b2c + c3 - abc - bc2 - c2a
= a3 + b3 + c3 -a2b + a2b - ca2 + a2c + bc2 - bc2 - ab2 + ab2 - abc - abc - abc + ac2 - ac2 + b2c - b2c
= a3 + b3 + c3 - 3abc
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