Finding Coefficient Values

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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...coefficient "n chooses i", which is defined as

C(n, i)=n!/[i!*(n-i)!]

For instance, C(3, 1)=3!/[1!*(3-1)!]=3!/(1!*2!)=3.

So,

(1-x)^3=C(3, 0)*1+C(3, 1)(-x)+C(3, 2)(-x)^2+C(3, 3) (-x)^3

=1-C(3, 1)x+C(3, 2)x^2-x^3

.....................................................................(1)
and

(1+x^2)^8=C(8, 0)*1+C(8, 1)(x^2)+C(8, 2)(x^2)^2+C(8, 3) (x^2)^3+...+C(8, 7)(x^2)^7+C(8,8)(x^2)^8
=1+C(8, 1)(x^2)+C(8, 2)(x^4)+C(8, 3) (x^6)+...+C(8, 7)(x^14)+x^16

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