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What is the coefficient of  \(x^3\)in this expression?

 

\((x^4+x^3+x^2+x+1)^4\)

 Oct 29, 2022
 #1
avatar
-1

Expanding, we get

(x^4 + x^3 + x^2 + x + 1)^4 = x^16 + 4x^15 + 12x^14 + 25x^13 + 38x^12 + 54x^11 + 68x^10 + 80x^9 + 85x^8 + 80x^7 + 68x^6 + 54x^5 + 38x^4 + 25x^3 + 12x^2 + 4x + 1

 

so the coefficient of x^3 is 25.

 Oct 29, 2022
 #4
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Sorry, incorrect

bugmenot  Oct 30, 2022
 #2
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+1

Expand   (x^4 + x^3 + x^2 + x + 1)^4:

 

x^16 + 4 x^15 + 10 x^14 + 20 x^13 + 35 x^12 + 52 x^11 + 68 x^10 + 80 x^9 + 85 x^8 + 80 x^7 + 68 x^6 + 52 x^5 + 35 x^4 + 20 x^3 + 10 x^2 + 4 x + 1
 

Coefficient of x^3 = 20

 Oct 29, 2022
 #3
avatar+17 
0

Thank you, correct!

bugmenot  Oct 30, 2022
edited by bugmenot  Oct 30, 2022

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