By how much does `3x^(3)-5x^(2)+2x-3` exceed `2x^(3)-3x^(2)+x+1`?

Answer

To find out by how much the expression \(3x^3 - 5x^2 + 2x - 3\) exceeds the expression \(2x^3 - 3x^2 + x + 1\), we will subtract the second expression from the first expression.

### Step-by-step Solution:

1. **Write down the expressions**:
We have:
\[ A = 3x^3 - 5x^2 + 2x - 3 \]
\[ B = 2x^3 - 3x^2 + x + 1 \]

2. **Set up the subtraction**:
We need to find \(A - B\):
\[ A - B = (3x^3 - 5x^2 + 2x - 3) - (2x^3 - 3x^2 + x + 1) \]

3. **Distribute the negative sign**:
When we subtract \(B\), we change the signs of each term in \(B\):
\[ A - B = 3x^3 - 5x^2 + 2x - 3 - 2x^3 + 3x^2 - x - 1 \]

4. **Combine like terms**:
Now, we will combine the like terms:
- For \(x^3\) terms: \(3x^3 - 2x^3 = 1x^3\)
- For \(x^2\) terms: \(-5x^2 + 3x^2 = -2x^2\)
- For \(x\) terms: \(2x - x = 1x\)
- For constant terms: \(-3 - 1 = -4\)

Putting it all together, we get:
\[ A - B = x^3 - 2x^2 + x - 4 \]

5. **Final result**:
Therefore, the expression \(3x^3 - 5x^2 + 2x - 3\) exceeds \(2x^3 - 3x^2 + x + 1\) by:
\[ x^3 - 2x^2 + x - 4 \]