Look at this sentence:
- next, we explain why the problem will be done this way.
Could we write the sentence adding the preposition "in" to?
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Both ways are fine. (math context)
Next, we explain why the problem will be done in this way.
This would be considered more formal. However, the in can be implied as in your example, thinking of it as follows. ( ) adds implied information.
Next, we explain why the problem will be done. (How?) This way.