#### Answer

$-2\sin 3x\cdot\sin x$

#### Work Step by Step

Sum-to-Product:
$\displaystyle \cos A-\cos B=-2\sin(\frac{A+B}{2})\sin(\frac{A-B}{2})$
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$\displaystyle \frac{A+B}{2}=\frac{4x+2x}{2}=3x$
$\displaystyle \frac{A-B}{2}=\frac{4x-2x}{2}=x$
$\cos 4x-\cos 2x=-2\sin 3x\cdot\sin x$