Simplify:
`4x^(3)-2x^(2)+5x-1+8x+x^(2)-6x^(3)+7-6x+3-3x^(2)-x^(3)`

Answer

To simplify the expression \( 4x^3 - 2x^2 + 5x - 1 + 8x + x^2 - 6x^3 + 7 - 6x + 3 - 3x^2 - x^3 \), we will follow these steps:

### Step 1: Rearrange the terms
Group the like terms together:
- Cubic terms: \( 4x^3 - 6x^3 - x^3 \)
- Quadratic terms: \( -2x^2 + x^2 - 3x^2 \)
- Linear terms: \( 5x + 8x - 6x \)
- Constant terms: \( -1 + 7 + 3 \)

### Step 2: Combine the cubic terms
Now, combine the cubic terms:
\[ 4x^3 - 6x^3 - x^3 = (4 - 6 - 1)x^3 = -3x^3 \]

### Step 3: Combine the quadratic terms
Next, combine the quadratic terms:
\[ -2x^2 + x^2 - 3x^2 = (-2 + 1 - 3)x^2 = -4x^2 \]

### Step 4: Combine the linear terms
Now, combine the linear terms:
\[ 5x + 8x - 6x = (5 + 8 - 6)x = 7x \]

### Step 5: Combine the constant terms
Finally, combine the constant terms:
\[ -1 + 7 + 3 = (-1 + 7 + 3) = 9 \]

### Step 6: Write the final simplified expression
Putting it all together, we have:
\[ -3x^3 - 4x^2 + 7x + 9 \]

### Final Answer:
The simplified expression is:
\[ -3x^3 - 4x^2 + 7x + 9 \]