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$(a-b) \times(a+b)=$
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Verified Answer
The correct answer is:
$2(\mathbf{a} \times \mathbf{b})$
$\begin{aligned}
(\mathbf{a}-\mathbf{b}) \times(\mathbf{a}+\mathbf{b})=\mathbf{a} \times \mathbf{a}-\mathbf{b} \times \mathbf{a}+ & \mathbf{a} \times \mathbf{b}-\mathbf{b} \times \mathbf{b} \\
& =\mathbf{a} \times \mathbf{b}-\mathbf{b} \times \mathbf{a}=\mathbf{a} \times \mathbf{b}+\mathbf{a} \times \mathbf{b}=2(\mathbf{a} \times \mathbf{b})
\end{aligned}$
(\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})
\end{aligned}$
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