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"expands the concept" is correct and usable in written English.
You can use it to indicate that something is broadening the idea or topic previously presented. For example, "The professor's lecture expands the concept of quantum mechanics by introducing the three principles of quantum theory."
Exact(23)
The method expands the concept of chaotic synchronization based on the stability criterion of linear systems, proposed earlier.
Unexpected and equally evocative work by Manuel Alvarez Bravo and William Gedney expands the concept, and Nair's film stills help pin it down.
This concert of canonical rock tunes, re-imagined and re-contextualized, expands the concept of a "cover tune" to be more than an homage to the original.
The ISAA model introduces the ontology-based semantic representation mode to the DR representation and expands the concept elements of IBIS.
This project expands the concept of the previously designed beta microprobe, which has been validated extensively in neurobiological experiments performed on anesthetized animals.
DJ Dolores, a D.J. and composer from Recife, Brazil (real name: Helder Aragão), draws on elements of Pernambucan folklore from deep within a sampling-and-scratching sensibility; his new band, Orchestra Santa Massa, expands the concept into live instruments.
Similar(36)
It may even expand the concept further.
He should, however, expand the concept.
Appreciation: How can we expand the concept of sacredness?
Mr. Kaufman is working on a plan that would expand the concept even further.
Jon is now poised to expand the concept to other cities.
More suggestions(16)
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expands the notion
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widened the concept
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broaden the concept
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com