10. Let $x=\cos \theta$. Express $\cos 3 \theta$ in terms of $x$.
10. $4 x^{3}-3 x$
$$
\begin{aligned}
\cos 3 \theta & =\cos (2 \theta+\theta) \\
& =\cos 2 \theta \cos \theta-\sin 2 \theta \sin \theta \\
& =\left(2 \cos ^{2} \theta-1\right) \cos \theta-2 \sin ^{2} \theta \cos \theta \\
& =\left(2 \cos ^{2} \theta-1\right) \cos \theta-2\left(1-\cos ^{2} \theta\right) \cos \theta \\
& =\left(2 x^{2}-1\right) x-2\left(1-x^{2}\right) x \\
& =4 x^{3}-3 x
\end{aligned}
$$