`vecA and vecB` are two vectors. `(vecA + vecB) xx (vecA - vecB)` can be expressed as :

Options

A. `2(vecB xx vecA)`
B. `-2(vecB xx vecA)`
C. `vecB xx vecA`
D. `vecA xx vecB`

Explanation

To solve the expression \((\vec{A} + \vec{B}) \times (\vec{A} - \vec{B})\), we can use the distributive property of the cross product. Here’s a step-by-step breakdown:

### Step 1: Expand the expression
Using the distributive property of the cross product, we can expand the expression:
\[ (\vec{A} + \vec{B}) \times (\vec{A} - \vec{B}) = \vec{A} \times \vec{A} - \vec{A} \times \vec{B} + \vec{B} \times \vec{A} - \vec{B} \times \vec{B} \]

### Step 2: Apply properties of the cross product
We know that the cross product of any vector with itself is zero:
\[ \vec{A} \times \vec{A} = \vec{0} \quad \text{and} \quad \vec{B} \times \vec{B} = \vec{0} \]
Thus, the expression simplifies to:
\[ \vec{0} - \vec{A} \times \vec{B} + \vec{B} \times \vec{A} - \vec{0} \]
This simplifies further to:
\[ -\vec{A} \times \vec{B} + \vec{B} \times \vec{A} \]

### Step 3: Use the anti-commutative property
The cross product is anti-commutative, meaning:
\[ \vec{B} \times \vec{A} = -(\vec{A} \times \vec{B}) \]
Substituting this into our expression gives:
\[ -\vec{A} \times \vec{B} - \vec{A} \times \vec{B} = -2(\vec{A} \times \vec{B}) \]

### Final Result
Thus, we can express \((\vec{A} + \vec{B}) \times (\vec{A} - \vec{B})\) as:
\[ -2(\vec{A} \times \vec{B}) \]

### Conclusion
The final answer is:
\[ (\vec{A} + \vec{B}) \times (\vec{A} - \vec{B}) = -2(\vec{A} \times \vec{B}) \]