How do I solve number 3b and c

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The discussion focuses on solving problems 3b and 3c, emphasizing that homework questions should be posted in designated sections and formatted using the homework template. For problem 3b, the key step is to expand the expression (t-2)^2 and combine it with other terms. The solution for problem 3c should utilize the answer obtained from problem 3a. Participants are reminded to type out their work instead of posting images. Proper formatting and adherence to guidelines are crucial for effective assistance.
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Your work looks find for problem 3b. What do you get for problem 3c?

Note that homework questions must be posted in one of the Homework sections, not in the technical math section. For such problems, you must also use the homework template. Please refrain from posting images of your work. Instead, type the problem and your work.
 
For 3b, I think the goal is to actually expand the expressions in the parenthesis, starting with (t-2)^2 = t^2 + ? t + ? ..., then combine with the remaining terms. For 3c, use the answer from 3a.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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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