SOLUTION: Find the coefficient of x^22 in the expansion of (1-3x)(1+x^3)^10.

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Question 1187142: Find the coefficient of x^22 in the expansion of (1-3x)(1+x^3)^10.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The expansion of %28y%2B1%29%5E10 is
%28y%2B1%29%5E10=y%5E10=10y%5E9%2B45y%5E8%2B120y%5E7%2B210y%5E6%2B%22...%22 where the coefficient of y%5E7 is 10%2A9%2A8%2F%283%2A2%29=120 .
With x%5E3=y it is
%28x%5E3%2B1%29%5E10=x%5E30=10x%5E27%2B45x%5E24%2B120x%5E21%2B210x%5E18%2B%22...%22
When that is multiplied times %281-3x%29 the term in x%5E22 will be
%28-3x%29%28120x%5E21%29=-360x%5E22
The coefficient of x%5E22 is highlight%28-360%29 .