`(-a-b)(b-a)` is

Options

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

Answer

To solve the expression \((-a-b)(b-a)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s the step-by-step solution:

### Step 1: Rewrite the expression
We start with the expression:
\[ (-a - b)(b - a) \]

### Step 2: Apply the distributive property
We will distribute each term in the first bracket to each term in the second bracket:
\[ (-a)(b) + (-a)(-a) + (-b)(b) + (-b)(-a) \]

### Step 3: Calculate each term
Now we will calculate each of the products:
1. \((-a)(b) = -ab\)
2. \((-a)(-a) = a^2\)
3. \((-b)(b) = -b^2\)
4. \((-b)(-a) = ab\)

### Step 4: Combine the results
Now we combine all the terms we calculated:
\[ -ab + a^2 - b^2 + ab \]

### Step 5: Simplify the expression
Notice that \(-ab\) and \(ab\) are like terms and they cancel each other out:
\[ a^2 - b^2 \]

### Final Result
Thus, the simplified expression is:
\[ a^2 - b^2 \]