Take `m^(2) + m + 4` from `-m^(2) + 3m + 6` and the result from `m^(2) + m + 1`.

Answer

To solve the problem step by step, we will follow the instructions provided in the question.

### Step 1: Subtract \( m^2 + m + 4 \) from \( -m^2 + 3m + 6 \)

We start with the expression:
\[ -m^2 + 3m + 6 \]
We need to subtract \( m^2 + m + 4 \) from it. This means we will rewrite the expression as:
\[ -m^2 + 3m + 6 - (m^2 + m + 4) \]
Now, distribute the negative sign:
\[ -m^2 + 3m + 6 - m^2 - m - 4 \]

### Step 2: Combine like terms

Now, we will combine the like terms:
- For \( m^2 \):
\(-m^2 - m^2 = -2m^2\)
- For \( m \):
\(3m - m = 2m\)
- For the constant:
\(6 - 4 = 2\)

Putting it all together, we get:
\[ -2m^2 + 2m + 2 \]

### Step 3: Subtract the result from \( m^2 + m + 1 \)

Now we need to subtract the result we obtained from \( m^2 + m + 1 \):
\[ m^2 + m + 1 - (-2m^2 + 2m + 2) \]
This can be rewritten as:
\[ m^2 + m + 1 + 2m^2 - 2m - 2 \]

### Step 4: Combine like terms again

Now, we will combine the like terms:
- For \( m^2 \):
\(m^2 + 2m^2 = 3m^2\)
- For \( m \):
\(m - 2m = -m\)
- For the constant:
\(1 - 2 = -1\)

Putting it all together, we get:
\[ 3m^2 - m - 1 \]

### Final Answer
Thus, the final result is:
\[ 3m^2 - m - 1 \]

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