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

• Frogeyedpeas
In summary, the conversation revolved around finding the resultant expression when multiplying the cubic formula by 3a, adding +b, and then cubing the entire thing. One person suggested writing down the equation of a cubic polynomial and using normal algebra, while another person clarified that the cubic formula refers to the general solution for the roots of a cubic polynomial. They also provided a link to the formula.
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

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

Last edited by a moderator:

## 1. What does it mean to "cube the entire thing" in this context?

When we cube a number or expression, we are multiplying it by itself three times. In this case, we would be cubing the result of adding 3a and b together.

## 2. How do you add 3a and b together?

To add 3a and b, we simply combine the two terms. Since they have different variables (a and b), we cannot simplify any further.

## 3. Can this expression be simplified further?

No, this expression cannot be simplified any further. We have already added the terms and cubed the result, leaving us with a final expression of (3a + b)^3.

## 4. Is there a specific order for performing the addition and cubing?

Yes, there is a specific order for performing these operations. We must first add 3a and b together, and then cube the result. If we were to cube 3a and b separately, we would get a different result.

## 5. Can you provide an example of how to solve this expression?

Sure. Let's say we have the expression 3a + b = 5. We would first add 3a and b together, giving us 3a + b = 5. Then, we cube the result, giving us (3a + b)^3 = 125. So, the final expression is (3a + b)^3 = 125.

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