Subtract:
`- m^(2) + 5mn` from `4m^(2) - 3mn + 8`

Answer

To solve the problem of subtracting `-m^2 + 5mn` from `4m^2 - 3mn + 8`, we will follow these steps:

### Step 1: Write down the expression
We need to subtract `-m^2 + 5mn` from `4m^2 - 3mn + 8`. This can be expressed mathematically as:
\[ (4m^2 - 3mn + 8) - (-m^2 + 5mn) \]

### Step 2: Distribute the negative sign
When we subtract an expression, we can distribute the negative sign across the terms in the expression being subtracted. This means:
\[ -(-m^2 + 5mn) = m^2 - 5mn \]

So, the expression now becomes:
\[ 4m^2 - 3mn + 8 + m^2 - 5mn \]

### Step 3: Combine like terms
Now, we will combine the like terms. The like terms are:
- The \(m^2\) terms: \(4m^2 + m^2\)
- The \(mn\) terms: \(-3mn - 5mn\)
- The constant term: \(8\)

Calculating these:
1. For \(m^2\) terms:
\[ 4m^2 + m^2 = 5m^2 \]
2. For \(mn\) terms:
\[ -3mn - 5mn = -8mn \]
3. The constant term remains as:
\[ 8 \]

### Step 4: Write the final expression
Putting it all together, we have:
\[ 5m^2 - 8mn + 8 \]

Thus, the final answer is:
\[ 5m^2 - 8mn + 8 \]

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