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

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Discussion Overview

The discussion revolves around the manipulation of the cubic formula, specifically how to express it after multiplying by 3a, adding b, and then cubing the entire expression. The scope includes algebraic manipulation and the understanding of cubic polynomials.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for the resultant expression after performing specific algebraic operations on the cubic formula.
  • Another participant suggests writing down the equation of a cubic polynomial and performing the operations using standard algebra.
  • A clarification is requested regarding the term "the cubic formula," with one participant indicating a possible misunderstanding about whether it refers to a cubic polynomial.
  • A participant explains their intention to rewrite the cubic formula into a specific form, providing a general cubic polynomial equation and a link to a resource for the cubic formula.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the interpretation of "the cubic formula," and there are multiple viewpoints regarding the approach to the problem.

Contextual Notes

There are unresolved assumptions about the definitions of terms used, particularly "the cubic formula," and the specific operations to be performed on it.

Frogeyedpeas
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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
 
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Frogeyedpeas said:
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.
 
berkeman said:
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?
 
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
 
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