Subtract `5x^(2) - 3xy + 2y^(2) "from " 7x^(2) - 5xy - 8y^(2)`.

Answer

To solve the problem of subtracting \(5x^{2} - 3xy + 2y^{2}\) from \(7x^{2} - 5xy - 8y^{2}\), we can follow these steps:

### Step 1: Write the expression to subtract
We start with the expression we want to subtract from:
\[ 7x^{2} - 5xy - 8y^{2} \]
and we need to subtract:
\[ 5x^{2} - 3xy + 2y^{2} \]

### Step 2: Change the subtraction to addition
To perform the subtraction, we can rewrite it as:
\[ 7x^{2} - 5xy - 8y^{2} - (5x^{2} - 3xy + 2y^{2}) \]
This means we will distribute the negative sign across the second expression:
\[ = 7x^{2} - 5xy - 8y^{2} - 5x^{2} + 3xy - 2y^{2} \]

### Step 3: Combine like terms
Now we will combine like terms. Like terms are those that have the same variables raised to the same powers.

1. Combine \(x^{2}\) terms:
\[ 7x^{2} - 5x^{2} = 2x^{2} \]

2. Combine \(xy\) terms:
\[ -5xy + 3xy = -2xy \]

3. Combine \(y^{2}\) terms:
\[ -8y^{2} - 2y^{2} = -10y^{2} \]

### Step 4: Write the final expression
Putting it all together, we have:
\[ 2x^{2} - 2xy - 10y^{2} \]

### Final Answer
The result of subtracting \(5x^{2} - 3xy + 2y^{2}\) from \(7x^{2} - 5xy - 8y^{2}\) is:
\[ \boxed{2x^{2} - 2xy - 10y^{2}} \]