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(B) The sum of the coefficients of a polynomial $P(x)$ is obtained by setting all variables equal to $1$.For the first expansion $(\alpha x^2 - 2x + 1

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$1$

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(B) The sum of the coefficients of a polynomial $P(x)$ is obtained by setting all variables equal to $1$.For the first expansion $(\alpha x^2 - 2x + 1)^{35}$,the sum of coefficients is $(\alpha(1)^2 - 2(1) + 1)^{35} = (\alpha - 2 + 1)^{35} = (\alpha - 1)^{35}$.For the second expansion $(x - \alpha y)^{35}$,the sum of coefficients is $(1 - \alpha(1))^{35} = (1 - \alpha)^{35}$.Given that these sums are equal: $(\alpha - 1)^{35} = (1 - \alpha)^{35}$.Since $35$ is an odd integer,$(1 - \alpha)^{35} = -(\alpha - 1)^{35}$.Thus,$(\alpha - 1)^{35} = -(\alpha - 1)^{35}$,which implies $2(\alpha - 1)^{35} = 0$.Therefore,$(\alpha - 1)^{35} = 0$,which gives $\alpha - 1 = 0$,so $\alpha = 1$.

If the sum of the coefficients in the expansion of $(\alpha x^2 - 2x + 1)^{35}$ is equal to the sum of the coefficients in the expansion of $(x - \alpha y)^{35}$,then $\alpha = $

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