The sum of the coefficients in the expansion of `(1+x-3x^2)^(171)` is

Options

A. a) 0
B. b) 1
C. c) `-1`
D. d) 2

Answer

To find the sum of the coefficients in the expansion of \( (1 + x - 3x^2)^{171} \), we can follow these steps:

### Step 1: Understand the Sum of Coefficients
The sum of the coefficients in a polynomial can be found by substituting \( x = 1 \) into the polynomial. This is because substituting \( x = 1 \) effectively adds up all the coefficients.

### Step 2: Substitute \( x = 1 \)
We substitute \( x = 1 \) into the expression \( (1 + x - 3x^2)^{171} \):
\[ (1 + 1 - 3(1)^2)^{171} \]

### Step 3: Simplify the Expression
Now, simplify the expression inside the parentheses:
\[ 1 + 1 - 3(1) = 1 + 1 - 3 = 2 - 3 = -1 \]
Thus, we have:
\[ (-1)^{171} \]

### Step 4: Evaluate the Power
Since \( 171 \) is an odd number, we know that:
\[ (-1)^{171} = -1 \]

### Conclusion
Therefore, the sum of the coefficients in the expansion of \( (1 + x - 3x^2)^{171} \) is:
\[ \boxed{-1} \]