Question

Perform the operations.
negative left bracket 3 z squared plus 5 z minus left parenthesis 2 z squared minus 9 z right parenthesis right bracket plus left bracket left parenthesis 9 z squared minus left bracket 5 z minus z squared right bracket right parenthesis plus 4 z squared right bracket

Answer 1

Let's simplify the given expression step by step. The expression is:

\[
-\left(3z^2 + 5z - (2z^2 - 9z)\right) + \left((9z^2 - (5z - z^2)) + 4z^2\right)
\]

### Step 1: Simplify the first part
First, handle the expression inside the first set of parentheses:

1. Start with \( -(2z^2 - 9z) \):
\[
-(2z^2 - 9z) = -2z^2 + 9z
\]

2. Substitute back into the expression:
\[
3z^2 + 5z - (2z^2 - 9z) = 3z^2 + 5z - 2z^2 + 9z
\]

3. Combine like terms:
\[
(3z^2 - 2z^2) + (5z + 9z) = 1z^2 + 14z = z^2 + 14z
\]

4. Now apply the negative sign:
\[
-(z^2 + 14z) = -z^2 - 14z
\]

### Step 2: Simplify the second part
Now simplify the second part:
1. Start with \( 9z^2 - (5z - z^2) \):
\[
-(5z - z^2) = -5z + z^2
\]

2. Substitute back into the expression:
\[
9z^2 - (5z - z^2) = 9z^2 - 5z + z^2
\]

3. Combine like terms:
\[
(9z^2 + 1z^2) - 5z = 10z^2 - 5z
\]

4. Now add \( 4z^2 \):
\[
10z^2 - 5z + 4z^2 = (10z^2 + 4z^2) - 5z = 14z^2 - 5z
\]

### Step 3: Combine both parts
Now combine the results from both parts:
\[
-z^2 - 14z + (14z^2 - 5z)
\]

### Step 4: Combine like terms
Combine all like terms:
1. Combine \( -z^2 + 14z^2 \):
\[
14z^2 - z^2 = 13z^2
\]

2. Combine \( -14z - 5z \):
\[
-14z - 5z = -19z
\]

So the final simplified expression is:

\[
\boxed{13z^2 - 19z}
\]