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Question

Question: \[(\mathbf{a} - \mathbf{b}) \times (\mathbf{a} + \mathbf{b}) =\]...

(a−b)×(a+b)=(\mathbf{a} - \mathbf{b}) \times (\mathbf{a} + \mathbf{b}) =

A

2(a×b)2(\mathbf{a} \times \mathbf{b})

B

a×b\mathbf{a} \times \mathbf{b}

C

a2−b2a^{2} - b^{2}

D

None of these

Answer

2(a×b)2(\mathbf{a} \times \mathbf{b})

Explanation

Solution

(a−b)×(a+b)=a×a−b×a+a×b−b×b=a×b−b×a=a×b+a×b=2(a×b).(\mathbf{a} - \mathbf{b}) \times (\mathbf{a} + \mathbf{b}) = \mathbf{a} \times \mathbf{a} - \mathbf{b} \times \mathbf{a} + \mathbf{a} \times \mathbf{b} - \mathbf{b} \times \mathbf{b} = \mathbf{a} \times \mathbf{b} - \mathbf{b} \times \mathbf{a} = \mathbf{a} \times \mathbf{b} + \mathbf{a} \times \mathbf{b} = 2(\mathbf{a} \times \mathbf{b}).