Example 9. Simplify $1-\frac{1}{4} \sin ^{2} 2 \alpha-\sin ^{2} \beta-\cos ^{4} \alpha$ into a product form of trigonometric functions. (84 College Entrance Examination for Liberal Arts)

(84年高考文科试题) 

Note: The last line is kept in Chinese as it is a reference to the source of the problem and does not need to be translated. If you prefer it in English, it would be: (84 College Entrance Examination for Liberal Arts)
$$
\begin{aligned}
\text { Original expression }= & \left(1-\sin ^{2} \beta\right)-\frac{1}{4} \sin ^{2} 2 \alpha \\
& -\cos ^{4} \alpha \\
= & \cos ^{2} \beta-\sin ^{2} \alpha \cos ^{2} \alpha \\
& \left.\quad-\cos ^{4} \alpha\right) \\
= & \cos ^{2} \beta-\cos ^{2} \alpha\left(\sin ^{2} \alpha\right. \\
& \quad+\cos ^{2} \alpha \\
= & \cos ^{2} \beta-\cos ^{2} \alpha \\
= & \sin (\alpha+\beta) \sin (\alpha-\beta) .
\end{aligned}
$$