Solving a Dumb Math Question: Simplifying Equations with Variables

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AI Thread Summary
The discussion centers on simplifying the equation a=2bc^3 by substituting b with c/f. The user is unsure if the expression simplifies to (2c^4)/f or remains as is due to the brackets. The correct simplification is confirmed as (2c^4)/f, as c multiplied by c^3 equals c^4. The user expresses gratitude for the clarification, indicating a successful resolution to the problem. The conversation highlights the importance of understanding variable substitution and simplification in algebra.
Roscoe1989
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Homework Statement


Ok, so I have a=2bc^3 and b= c/f but I want to get rid of the b's.


Homework Equations



So I know I do a=2(c/f)c^3

The Attempt at a Solution



This is where I get lost (and feel stupid). Does this get simplified to (2c^4)/f? Or, is does it stay the same because the (c/f) is in brackets. I have to differentiate after, which is in itself another problem.
Thanks!
 
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Roscoe1989 said:

Homework Statement


Ok, so I have a=2bc^3 and b= c/f but I want to get rid of the b's.


Homework Equations



So I know I do a=2(c/f)c^3

The Attempt at a Solution



This is where I get lost (and feel stupid). Does this get simplified to (2c^4)/f? Or, is does it stay the same because the (c/f) is in brackets. I have to differentiate after, which is in itself another problem.
Thanks!

The bolded answer is correct. c * c^3 = c^4
 
Booya! Thank you, berkeman!
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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