I found this grammar point quite confusing at a first glance, but I felt like the example in Game Gengo’s N4 Video Textbook (it’s a long video, the relevant part starts at 2:59:30) explained it nicely.
Even after watching the Game Gengo example, I still don’t get this grammar point. What stands out to me is this bit from Bunpro: “This nuance is usually that ‘(A) happened and then went’, or ‘will happen, and then go’.”
That phrasing sounds a bit odd, and as someone who doesn’t know what it’s supposed to get across… yeah.
The phrasing is odd and you’re better off ignoring it, especially since the verb いく is supposed to be happening concurrently with the verb it attaches to (for example, 持っていく= lit: to hold and go, aka, to take).
This grammar point has two main meanings/usage.
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Progression or Change Over Time (Gradual transformation)
"Something continues to change or develop moving forward."
Often used for natural changes, trends, or future developments.
Frequently translated as “going to” or "continue"
E.g. これから気温が下がっていくでしょう。
→ The temperature is going to drop from now on.
2. Movement Away from the Speaker (Physical or Abstract)
“An action happens in a direction away from the speaker.”
This is literally about physical movement or metaphorically about emotional/psychological distance.
E.g. 明日、教科書を持っていくのを忘れないでね。
→ Don’t forget to take your textbook (with you) tomorrow.
持っていく=to take something (away from the speaker’s location) to another place.