Vector Proof - Dot and Cross Products

Hello everyone,

I am having some trouble with the following problem and would appreciate help. Thank you!

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16. For any vectors $\displaystyle \vec{a}, \vec{b}, \vec{c} $, show that $\displaystyle (\vec{a} \times \vec{b}) \times \vec{c} = (\vec{a} \bullet \vec{c})\vec{b} - (\vec{b} \bullet \vec{c})\vec{a} $.

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I worked on the RS since it is more complicated:

RS = $\displaystyle (|\vec{a}||\vec{c}|\cos \theta)\vec{b} - (|\vec{b}||\vec{c}|\cos \theta)\vec{a}) $

However, I do not know how to distribute the vectors $\displaystyle \vec{b} $ and $\displaystyle \vec{a} $ into the dot products.