Let $\bold{a}$ and $\bold{b}$ be three-dimensional vectors.  Then
\[(5 \bold{a} + 7 \bold{b}) \times (-\bold{a} + 3 \bold{b}) = k \bold{a} \times \bold{b}\]for some scalar $k$.  Find $k$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\bold{a}$ and $\bold{b}$ be three-dimensional vectors.  Then
\[(5 \bold{a} + 7 \bold{b}) \times (-\bold{a} + 3 \bold{b}) = k \bold{a} \times \bold{b}\]for some scalar $k$.  Find $k$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
22
Let $\bold{a}$ and $\bold{b}$ be three-dimensional vectors.  Then
\[(5 \bold{a} + 7 \bold{b}) \times (-\bold{a} + 3 \bold{b}) = k \bold{a} \times \bold{b}\]for some scalar $k$.  Find $k$.
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