Subtract
`-2a^2-2b^2 " from " -a^2-b^2+2ab`.

Options

A. `a^2-b^2-2ab`
B. `a^2-b^2+2ab`
C. `a^2+b^2+2ab`
D. `a^2-b^2`

Answer

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

### Step 1: Write the expression to be subtracted
We start with the expression we want to subtract from:
\[ -a^2 - b^2 + 2ab \]
Now, we need to subtract \(-2a^2 - 2b^2\) from it. We can write this as:
\[ -a^2 - b^2 + 2ab - (-2a^2 - 2b^2) \]

### Step 2: Simplify the subtraction
When we subtract a negative, it becomes addition:
\[ -a^2 - b^2 + 2ab + 2a^2 + 2b^2 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- For \(a^2\) terms: \(-a^2 + 2a^2 = (2 - 1)a^2 = a^2\)
- For \(b^2\) terms: \(-b^2 + 2b^2 = (2 - 1)b^2 = b^2\)
- The \(2ab\) term remains as it is.

Putting it all together, we have:
\[ a^2 + b^2 + 2ab \]

### Final Answer
Thus, the result of subtracting \(-2a^2 - 2b^2\) from \(-a^2 - b^2 + 2ab\) is:
\[ a^2 + b^2 + 2ab \]

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