# 3a, add +b and then cube the entire thing?

A quick question... what is the resultant expression if you multiply the cubic formula by 3a, add +b and then cube the entire thing?

Much appreciated

berkeman
Mentor
A quick question... what is the resultant expression if you multiply the cubic formula by 3a, add +b and then cube the entire thing?

Much appreciated
Pi.

Cool problem. Thanks.

chiro
Pi.

Cool problem. Thanks.
Aside from delicious pi, have you tried just writing the equation of a cubic polynomial down and then doing your operations using normal algebra?

HallsofIvy
Homework Helper
To clarify, what do you mean by "the cubic formula"? chiro seems to think you mean just a cubic polynomial. Is that correct?

I'm trying to rewrite the cubic formula (the general solution for the roots of a cubic polynomial into the form (3ax +b)^3 = ...

Where normally given a cubic polynomial equation

ax^3 + bx^2 + cx + d = 0

The answer can be found by making the substitution:

a = b/a

b = c/a

c = d/a

and then the formula is in this link:

http://planetmath.org/encyclopedia/CubicFormula.html [Broken]

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