$$T_k = \,^{100}C_k \cdot x^{100-k} \quad \text{for} \quad k = 0, 1, 2, \ldots 100$$
Then, what will be the value of
$$\Bigl (T_0 - T_2 + T_4 - \cdots + T_{100} \Bigr )^2 + \Bigl (T_1 - T_3 + T_5 - \cdots - T_{99} \Bigr )^2$$
The answer should be in terms of $x$