# Coefficient

Please show me how to find the coefficient of x^11 in (1-x)^n * (1+x^2)^2m .

Thank you.

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#### Solution Preview

Please show me how to find the coefficient of x^11 in (1-x)^n * (1+x^2)^2m .

Solution. You must specify the values of n and m. Otherwise, it is impossible to compute the coefficient of x^11 in general. Now I will show you the idea how to get the coefficient of x^11 by taking

n=3 and m=4

which means that (1-x)^n * (1+x^2)^2m = (1-x)^3 * (1+x^2)^8

We will mainly rely on the binomial formula:

(a+b)^n=C(n, 0)a^n +C(n, 1) a^(n-1)b+ C(n, 2)a^(n-2)b^2+...+C(n, n-1)ab^(n-1)+C(n, n)b^n

=a^n +C(n, 1) a^(n-1)b+ C(n, 2)a^(n-2)b^2+...+C(n, n-1)ab^(n-1)+b^n

where C(n, i) is the binomial ...

#### Solution Summary

This provides an example of finding a coefficient for a given polynomial.