Expanding, we get
\begin{align*}
(2 \mathbf{b} - \mathbf{a}) \times (3 \mathbf{c} + \mathbf{a}) &= 6 \mathbf{b} \times \mathbf{c} + 2 \mathbf{b} \times \mathbf{a} - 3 \mathbf{a} \times \mathbf{c} - \mathbf{a} \times \mathbf{a} \\
&= 6 \mathbf{b} \times \mathbf{c} - 2 \mathbf{a} \times \mathbf{b} - 3 \mathbf{a} \times \mathbf{c} - \mathbf{0} \\
&= 6 \begin{pmatrix} 1 \\ - 7 \\ 18 \end{pmatrix} - 2 \begin{pmatrix} 6 \\ - 7 \\ 3 \end{pmatrix} - 3 \begin{pmatrix} 4 \\ 7 \\ 2 \end{pmatrix} \\
&= \boxed{\begin{pmatrix} -18 \\ -49 \\ 96 \end{pmatrix}}.
\end{align*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{a},$ $\mathbf{b},$ $\mathbf{c}$ be three vectors such that
\[\mathbf{a} \times \mathbf{b} = \begin{pmatrix} 6 \\ -7 \\ 3 \end{pmatrix}, \quad \mathbf{a} \times \mathbf{c} = \begin{pmatrix} 4 \\ 7 \\ 2 \end{pmatrix}, \quad \mathbf{b} \times \mathbf{c} = \begin{pmatrix} 1 \\ -7 \\ 18 \end{pmatrix}.\]Compute $(2 \mathbf{b} - \mathbf{a}) \times (3 \mathbf{c} + \mathbf{a}).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} -18 \\ -49 \\ 96 \end{pmatrix}
Let $\mathbf{a},$ $\mathbf{b},$ $\mathbf{c}$ be three vectors such that
\[\mathbf{a} \times \mathbf{b} = \begin{pmatrix} 6 \\ -7 \\ 3 \end{pmatrix}, \quad \mathbf{a} \times \mathbf{c} = \begin{pmatrix} 4 \\ 7 \\ 2 \end{pmatrix}, \quad \mathbf{b} \times \mathbf{c} = \begin{pmatrix} 1 \\ -7 \\ 18 \end{pmatrix}.\]Compute $(2 \mathbf{b} - \mathbf{a}) \times (3 \mathbf{c} + \mathbf{a}).$
test