Suppose that for some a,b,c we have a+b+c = 6, ab+ac+bc = 5 and abc = 12. What is a^3+b^3+c^3?
+133 Oh, so convenient! (a^3+b^3+c^3) - (a+b+c)^3 = -3(a+b)(b+c)(a+c).
How convenient! (a+b)(b+c)(a+c) + abc = (a+b+c)(ab+ac+bc).
With these elusive factoring tricks down, we substitute numbers.
(a^3+b^3+c^3) - 216 = -3(30 - 12) = -54
216-54 = 162.
