<s>[INST] Some formula related with factor of (a+b+c+d) I am looking for some math formula  
For example 
\begin{align}
& a^2 -b^2 = (a+b)(a-b) \\
&a^3 +b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2 - ab-bc-ca) 
\end{align}
First one related with factor a+b and the second one related with factor a+b+c 
then
How about some formula related with a,b,c,d 
i.e., is there are some equation factors into (a+b+c+d)?
 [/INST] It will be probably
$$a^4+b^4+c^4+d^4-b^2a^2-c^2a^2-d^2a^2-b^2c^2-b^2d^2-d^2c^2+16abcd=(a+b+c+d)(a^3+b^3+c^3+d^3-ba^2-ca^2-da^2-ac^2-bc^2-dc^2-ab^2-cb^2-db^2-ad^2-bd^2-cd^2+4bca+4bda+4cad+4bcd)$$
OR

$$\sum a^4 -\sum a^2b^2 +16abcd=(\sum a)(\sum a^3-\sum ab^2 +4\sum abc)$$
  $$$$
  $$\sum \text{ represents cyclic summation}$$

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