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

[Frogeyedpeas]

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]

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]

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

 

[Frogeyedpeas]

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