Subtract :
`3z^(2)-2z^(2)+7z -8` from `8-z-z^(2)`

Answer

To solve the problem of subtracting \( 3z^2 - 2z^2 + 7z - 8 \) from \( 8 - z - z^2 \), we can follow these steps:

### Step 1: Write down the expressions
We start with the two expressions:
- Expression to subtract from: \( 8 - z - z^2 \)
- Expression to subtract: \( 3z^2 - 2z^2 + 7z - 8 \)

### Step 2: Change the subtraction to addition
To subtract the second expression from the first, we can rewrite the operation as:
\[ (8 - z - z^2) - (3z^2 - 2z^2 + 7z - 8) \]
This can be simplified to:
\[ 8 - z - z^2 - (3z^2 - 2z^2 + 7z - 8) \]

### Step 3: Distribute the negative sign
Distributing the negative sign across the second expression gives us:
\[ 8 - z - z^2 - 3z^2 + 2z^2 - 7z + 8 \]

### Step 4: Combine like terms
Now we can combine like terms:
- Constant terms: \( 8 + 8 = 16 \)
- \( z^2 \) terms: \( -z^2 - 3z^2 + 2z^2 = -2z^2 \)
- \( z \) terms: \( -z - 7z = -8z \)

Putting it all together, we have:
\[ -2z^2 - 8z + 16 \]

### Step 5: Write the final answer
Thus, the final result of the subtraction is:
\[ -3z^2 - 8z + 16 \]