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0
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avatar+563 

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

 Jun 24, 2024
 #1
avatar+1230 
+1

I basically expanded everything out. 

\(120v^{18}-540u^{3}v^{13}-80uv^{15}+810u^{6}v^{8}+360u^{4}v^{10}-405u^{9}v^{3}-540u^{7}v^{5}+270u^{10}\)

 

hmmm...there is no u^2v^9 term. 

So the coefficient is just 0. 

 

So 0 is our answer. 

 

Thanks! :)

 Jun 24, 2024
 #2
avatar+85 
0

XD just expanding is definentaly(100% misspelled) a way to do it

shmewy  Jun 24, 2024
edited by shmewy  Jun 24, 2024
 #3
avatar+1230 
+1

I know there are smarter ways to do it...but I'm not smart...as my name suggests

We could simply just take a look at the factors. 

\((2u - 3*v^3)*5*(3u^3 - 2v^5)^3\) never has a term for v^9, so it's impossible. 

 

We can easily tell, but ummm...yeah....

XD :)

 

~NTS

NotThatSmart  Jun 24, 2024

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