<s>[INST] Prove using factor theorem. Using factor theorem, show that $a+b$,$b+c$ and $c+a$ are factors of 
$(a + b + c)^3$ - $(a^3 + b^3 + c^3)$
How do we go about solving this ?
Thanks in advance !
 [/INST] Let,$f(a)$=$(a+b+c)^3-(a^3+b^3+c^3)$
If $(a+b)$ is a factor,$f(-b)$ must be $0$ by factor theorem.
Putting $f(-b)$,we get,
$(-b+b+c)^3-(-b^3+b^3+c^3)$
$=c^3-c^3=0$.
Similarly prove the others.
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