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What is the coefficient of \(x\) in \((x^4+x^3+x^2+x+1)^4\)?

 Mar 28, 2022
 #1
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+2

 

think about which terms could be included

x^4, x^3, x^2  will all tead to terms the power of x bigger than 1

so the only bit that could be relevant is (x+1)^4

 

the general term in the expansion is   \(\binom{4}{n}x^n\)   where x can be 0,1,2,3,or 4

 

so the term you want is  \(\binom{4}{1}x^1=4x\)

 

so the coefficint of x is 4

 Mar 28, 2022
edited by Melody  Mar 28, 2022
 #2
avatar+48 
+1

Thank you Melody!

 Apr 4, 2022

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