<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] If a+b is a Factor then -b is a root and vice versa. so just set a=-b and you get $((-b)+b+c)^3 - ((-b)^3+b^3+c^3) =c^3-c^3 = 0$. Therefor a+b is a Factor. Same for a+c and b+c.....
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