We have,

(1 – 2x + x^{2})^{n} = (1 – x)^{2n} where, n is an even number.

So the middle term is (\( \dfrac{2n}{2}\) + 1) = (n + 1)^{th} term.

Now,

T_{n} = T_{n+1}

= ^{2n}C_{n} (-1)^{n} (x)^{n}

= \( \dfrac{(2n)!}{(n!)^2} (-1)^n x^n\)

Hence, the middle term is \( \dfrac{(2n)!}{(n!)^2} (-1)^n x^n\)

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