Simplify combining like terms:
`(3y^(2) +5y - 4) - (8y - y^(2) - 4)`

Answer

To simplify the expression `(3y^(2) + 5y - 4) - (8y - y^(2) - 4)`, we will follow these steps:

### Step 1: Distribute the negative sign
We start by distributing the negative sign across the second set of parentheses. This means we will change the signs of each term inside the parentheses.

\[ (3y^2 + 5y - 4) - (8y - y^2 - 4) = 3y^2 + 5y - 4 - 8y + y^2 + 4 \]

### Step 2: Combine like terms
Now, we will combine the like terms. Like terms are those that have the same variable raised to the same power.

1. **Combine \(y^2\) terms:**
- \(3y^2 + y^2 = 4y^2\)

2. **Combine \(y\) terms:**
- \(5y - 8y = -3y\)

3. **Combine constant terms:**
- \(-4 + 4 = 0\)

Putting it all together, we have:

\[ 4y^2 - 3y + 0 \]

### Step 3: Simplify the expression
Since adding zero does not change the value, we can simplify our expression further:

\[ 4y^2 - 3y \]

### Final Answer:
The simplified expression is:

\[ 4y^2 - 3y \]

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