Simplify the expression `8(x^(2)-x-1) + 5 (2x-2) - 3 (x^(2) +x - 1)`

Answer

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

### Step 1: Distribute the coefficients
We will multiply each term inside the parentheses by the coefficient outside.

1. \( 8(x^2 - x - 1) = 8x^2 - 8x - 8 \)
2. \( 5(2x - 2) = 10x - 10 \)
3. \( -3(x^2 + x - 1) = -3x^2 - 3x + 3 \)

Now, we can rewrite the expression with these results:
\[ 8x^2 - 8x - 8 + 10x - 10 - 3x^2 - 3x + 3 \]

### Step 2: Combine like terms
Next, we will group the like terms together.

- For \( x^2 \) terms: \( 8x^2 - 3x^2 \)
- For \( x \) terms: \( -8x + 10x - 3x \)
- For constant terms: \( -8 - 10 + 3 \)

This gives us:
\[ (8x^2 - 3x^2) + (-8x + 10x - 3x) + (-8 - 10 + 3) \]

### Step 3: Simplify each group
Now we will simplify each group of like terms.

1. \( 8x^2 - 3x^2 = 5x^2 \)
2. \( -8x + 10x - 3x = -1x \) or simply \( -x \)
3. \( -8 - 10 + 3 = -15 \)

Putting it all together, we have:
\[ 5x^2 - x - 15 \]

### Final Result
Thus, the simplified expression is:
\[ \boxed{5x^2 - x - 15} \]