To write plainly and concisely, choose show instead of the roundabout phrase serve to illustrate.
- These technological innovations show (not serve to illustrate) how the world has changed.
Other possibilities include demonstrate, explain, illustrate and make clear.
- Two case studies explain (or demonstrate, illustrate, make clear) how the different topics intersect with other aspects of culture.
- The video made clear (or demonstrated, explained, illustrated) how the sorting mechanism works.
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