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

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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.
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
To clarify, what do you mean by "the cubic formula"? chiro seems to think you mean just a cubic polynomial. Is that correct?
 
  • #5
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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