To factor $ cv+vx+bc+bx $ we can use factoring by grouping.
Group $ \color{blue}{ cv }$ with $ \color{blue}{ vx }$ and $ \color{red}{ bc }$ with $ \color{red}{ bx }$ then factor each group.
$$ \begin{aligned} cv+vx+bc+bx &= ( \color{blue}{ cv+vx } ) + ( \color{red}{ bc+bx }) = \\ &= \color{blue}{ v( c+x )} + \color{red}{ b( c+x ) } = \\ &= (v+b)(c+x) \end{aligned} $$