Check please. Just need to make sure I am doing this right.

Given$\displaystyle \vec{u}\cdot\vec{u}=8,\;\vec{v}\cdot\vec{v}=6,\; \vec{u}\cdot\vec{v}=7$

Find: $\displaystyle (3u-v)\cdot (u-3v)$

$\displaystyle (3u-v)\cdot (u-3v)\implies \\(3u-v)\cdot u-[(3u-v)\cdot 3v]\implies \\3u\cdot u-v\cdot u-[3u\cdot 3v-v\cdot 3v]\implies \\3(u\cdot u)-v\cdot u-9(u\cdot v)+3(v\cdot v)\implies \\3(8)-7-9(7)+3(6)\implies \\(3u-v)\cdot (u-3v)=-28$