## yet another important algebric identity

Several blogs ago,  I had suggested the use of a powerful fundamental algebraic identity:

$a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$.

Now, this identity becomes a basic applied tool in Algebra and Trigonometry and Number theory, perhaps.

A salient feature of mathematics is that mathematicians always try to generalize a technique or concept.

Can you generalize the above identity as follows (a proof is required please):

Let there be quantities a,b,c,d…then prove that

$a^{3}+b^{3}+c^{3}+d^{3}+\ldots -3(abc+bcd+abd+\ldots)$ is divisible by $(a+b+c+d+ \ldots)$ and also  find the quotient.