Factorize the following `|3a+b+c a^3+b^3+c^3a+b+c a^2+b^2+c^2a^4+b^4+c^4a^2+b^2+c^2a^3+b^3+c^3a^5+b^5+c^5|`

Explanation

`|{:(3,,a+b+c,,a^(3)+b^(3)+c^(3)),(a+b+c,,a^(2)+b^(2)+c^(2),,a^(4)+b^(4)+c^(4)),(a^(2)+b^(2)+c^(2),,a^(3)+b^(3)+c^(3),,a^(5)+b^(5)+c^(5)):}|`
`= |{:(3,,a+b+c,,a^(3)+b^(3)+c^(3)),(a+b+c,,a^(2)+b^(2)+c^(2),,a^(4)+b^(4)+c^(4)),(a^(2)+b^(2)+c^(2),,a^(3)+b^(3)+c^(3),,a^(5)+b^(5)+c^(5)):}|`
`=|underset(a^(2)" "b^(2)" "c^(2))underset(a" "b" "c)(1" "1" "1)||underset(a^(3)" "b^(3)" "c^(3))underset(a" "b" "c)(1" "1" "1)|`
`=[(a-b)(b-c)(c-a)][(a+b+c)(a-b)(b-c)(c-a)`
`=(a-b)^(2)(b-c)^(2)(c-a)^(2)(a+b+c)`