If the sum of the coefficient in the expansion of
` (alpha x^(2) - 2x + 1)^(35)` is equal to the sum of the coefficient of the
expansion of `(x - alpha y)^(35)`, then `alpha` =

Explanation

To solve the problem, we need to find the value of \( \alpha \) such that 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 \( (x - \alpha y)^{35} \).

### Step-by-Step Solution:

1. **Understanding the Sum of Coefficients:**
The sum of the coefficients of a polynomial \( P(x) \) can be found by substituting \( x = 1 \) into the polynomial. Thus, we will evaluate both expressions at \( x = 1 \) and \( y = 1 \).

2. **Calculate the Sum of Coefficients for the First Expression:**
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