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