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

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

In the formula, a^3+b^3+c^3-3 abc = 1/2 (a+b+c){(a-b)^2+(b-c)^2+(c-a)^2} , if a + b + c != 0 , Show that if a^3 +b^3+c^3= 3abc impliesa=b=c

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

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

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

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

Verify : a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]

a^(3)+b^(3)+c^(3)-3abc=k(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] , then k=

If a= 25, b= 15, c= - 10 then (a^(3) + b^(3) + c^(3) - 3abc)/((a-b)^(2) + (b-c)^(2) + (c-a)^(2))

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a)(a+b+c)