Subtract:
`5a^(2) - 7ab + 5b^(2) "from" 3ab - 2a^(2) - 2b^(2)`

Answer

To solve the problem of subtracting \(5a^{2} - 7ab + 5b^{2}\) from \(3ab - 2a^{2} - 2b^{2}\), we will follow these steps:

### Step 1: Write the expression to be subtracted
We start with the expression we need to subtract from:
\[ 3ab - 2a^{2} - 2b^{2} \]
We need to subtract:
\[ 5a^{2} - 7ab + 5b^{2} \]

### Step 2: Rewrite the subtraction
When we subtract one expression from another, we can rewrite it as:
\[ (3ab - 2a^{2} - 2b^{2}) - (5a^{2} - 7ab + 5b^{2}) \]

### Step 3: Distribute the negative sign
Distributing the negative sign across the second expression gives us:
\[ 3ab - 2a^{2} - 2b^{2} - 5a^{2} + 7ab - 5b^{2} \]

### Step 4: Combine like terms
Now we will combine the like terms:
- For \(ab\) terms: \(3ab + 7ab = 10ab\)
- For \(a^{2}\) terms: \(-2a^{2} - 5a^{2} = -7a^{2}\)
- For \(b^{2}\) terms: \(-2b^{2} - 5b^{2} = -7b^{2}\)

Putting it all together, we have:
\[ 10ab - 7a^{2} - 7b^{2} \]

### Step 5: Final expression
Thus, the final result of the subtraction is:
\[ 10ab - 7a^{2} - 7b^{2} \]