Killer #208

Hints
1. 2a²b²c² + (a³ + b³ + c³)abc + b³c³ + c³a³ + a³b³ ------Notice the hightlighted section

2. 2a²b²c² + a⁴bc + b⁴ac + c⁴ab + b³c³ + c³a³ + a³b³ ------It was expanded

3. 2a²b²c² + a⁴bc + b⁴ac + c⁴ab + b³c³ + c³a³ + a³b³------Notice the hightlighted section

4. 2a²b²c² + a⁴bc + abc(b³ + c³) + b³c³ + c³a³ + a³b³--------the common factors of "abc" were factored out

5. 2a²b²c² + a⁴bc + abc(b³ + c³) + b³c³ + c³a³ + a³b³------Notice the hightlighted section

6. 2a²b²c² + a⁴bc + abc(b³ + c³) + b³c³ + a³(b³ + c³)-------the common factor "a³" was factored out

7. 2a²b²c² + a⁴bc + b³c³ + abc(b³ + c³) + a³(b³ + c³)---------notice this selection

8. 2a²b²c² + a⁴bc + b³c³ + a(b³ + c³)(a² + bc)---------the common factors of "a(b³ + c³)" were factored out

9. 2a²b²c² + a⁴bc + b³c³ + a(b³ + c³)(a² + bc)---------notice this selection

10. bc(a⁴ + 2a²bc + b²c²) + a(b³ + c³)(a² + bc)---------"bc" was factored out

11. bc(a² + bc)² + a(b³ + c³)(a² + bc)---------"(a⁴ + 2a²bc + b²c²)" is a quadratic equation that can be foiled into "(a² + bc)²"

12. bc(a² + bc)² + a(b³ + c³)(a² + bc)---------notice

13. (a² + bc)[bc(a² + bc) + a(b³ + c³)]---------"(a² + bc)" was factored out

14. (a² + bc)[bc(a² + bc) + a(b³ + c³)]---------notice

15. (a² + bc)[bca² + b²c² + ab³ + ac³]---------expand

16. (a² + bc)[bca² + b²c² + ab³ + ac³]---------notice

17. (a² + bc)[bca² + ab³ + b²c² + ac³]---------notice

18. (a² + bc)[bca² + ab³ + c²(b² + ac)]---------c² was factored out

19. (a² + bc)[bca² + ab³ + c²(b² + ac)]---------notice

20. (a² + bc)[ba(ac + b²) + c²(b² + ac)]---------notice

21. (a² + bc)[ba(b² + ac) + c²(b² + ac)]---------switch the two terms "ac + b²" around

22. (a² + bc)[ba(b² + ac) + c²(b² + ac)]---------notice

23. (a² + bc)[(b² + ac)(ba + c²)]---------"b² + ac" was factored out