Question

Verify,(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc.​

Answer 1

Answer:

(a+b+c)(a²+b²+c²-ab-bc-ca)

=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-a²c+a²b+b³+bc²-ab²-b²c-abc+a²c+b²c+c³-abc-bc²-ac²

=a³+b³+c³-3abc

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