Subtract : `x^(3) + 3x^(2) - 5x + 4` from `3x^(3) - x^(2) + 2x - 4`

Answer

To solve the problem of subtracting \( x^3 + 3x^2 - 5x + 4 \) from \( 3x^3 - x^2 + 2x - 4 \), we will follow these steps:

### Step-by-Step Solution:

1. **Write down the expressions**:
We have the first expression \( 3x^3 - x^2 + 2x - 4 \) and we need to subtract the second expression \( x^3 + 3x^2 - 5x + 4 \) from it.

\[ (3x^3 - x^2 + 2x - 4) - (x^3 + 3x^2 - 5x + 4) \]

2. **Distribute the negative sign**:
When we subtract the second expression, we need to change the signs of each term in that expression.

\[ 3x^3 - x^2 + 2x - 4 - x^3 - 3x^2 + 5x - 4 \]

3. **Combine like terms**:
Now, we will combine the coefficients of like terms (the terms with the same power of \( x \)).

- For \( x^3 \):
\[ 3x^3 - x^3 = (3 - 1)x^3 = 2x^3 \]

- For \( x^2 \):
\[ -x^2 - 3x^2 = (-1 - 3)x^2 = -4x^2 \]

- For \( x \):
\[ 2x + 5x = (2 + 5)x = 7x \]

- For the constant terms:
\[ -4 - 4 = -8 \]

4. **Write the final expression**:
Combining all the simplified terms gives us the final result.

\[ 2x^3 - 4x^2 + 7x - 8 \]

### Final Answer:
The result of subtracting \( x^3 + 3x^2 - 5x + 4 \) from \( 3x^3 - x^2 + 2x - 4 \) is:

\[ \boxed{2x^3 - 4x^2 + 7x - 8} \]