The sum of the coefficients in the expansion of `(5x-4y)^(n)`, where n is a positive integer, is

Options

A. 0
B. n
C. 1
D. `-1`

Answer

To find the sum of the coefficients in the expansion of \((5x - 4y)^n\), where \(n\) is a positive integer, 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 \(x = 1\) and \(y = 1\) into the polynomial. This is because substituting these values effectively adds all the coefficients together.

### Step 2: Substitute \(x\) and \(y\)
We substitute \(x = 1\) and \(y = 1\) into the expression \((5x - 4y)^n\):
\[ (5(1) - 4(1))^n \]

### Step 3: Simplify the Expression
Now simplify the expression:
\[ (5 - 4)^n = (1)^n \]

### Step 4: Evaluate the Expression
Since \(1^n = 1\) for any positive integer \(n\), the sum of the coefficients is:
\[ 1 \]

### Final Answer
Thus, the sum of the coefficients in the expansion of \((5x - 4y)^n\) is \(1\).

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