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Prove that a^3+b^3+c^3-3abc=1/2(a+b+c){(...

Prove that `a^3+b^3+c^3-3abc=1/2(a+b+c){(a-b)^2+(b-c)^2+(c-a)^2}`

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Given,
`1/2(a+b+c){(a-b)^2+(b-c)^2+(c-a)^2}`
`=>1/2(a+b+c){a^2-2ab+b^2+b^2-2bc+c^2+c^2-2ac+a^2}`
`=>1/2(a+b+c){2a^2+2b^2+2c^2-2ab-2bc-2ca}`
`=>(a+b+c){a^2+b^2+c^2-ab-bc-ca}`
`=>a^3+ab^2+ac^2-a^2b-abc-ca^2+a^2+b^3+c^2b-ab^2-b^2c-abc-a^2c-b^2c-c^3-abc-bc^2-ac^2`
`=>a^3+b^3+c^3−3abc`
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