Learn Hardcore Russian: Для поездки я взял дополнительный чемодан. - I took an additional suitcase for the trip.

The preposition для always takes the genitive case in Russian. Since поездка is a feminine noun, its genitive singular form is поездки. So для поездки literally means for the trip.

Could I say в поездку instead of для поездки?

Yes. Both для поездки and в поездку can express purpose, but with a slight nuance:

для поездки (“for the trip”) emphasizes the purpose or intended use.
в поездку (“into the trip” or “on the trip”) highlights the direction/moment of going.
You can rephrase the sentence as В поездку я взял дополнительный чемодан, and it will still sound natural.

What is the difference between взять and брать, and why is взял used here?

Russian has two aspectual pairs for “to take”:

брать (imperfective): used for habitual or ongoing actions (e.g. “I was taking”).
взять (perfective): used for a single, completed action (“I took”).
Since the speaker refers to a one-off completed action in the past, they use the perfective взял.

Why is взял in the masculine form, and what would a woman say?

In the Russian past tense, verbs agree with the speaker’s gender:

A man says я взял.
A woman says я взяла.
(Neuter взяло is used with “it,” and взяли for “we/they.”)

Why does дополнительный чемодан look exactly like the nominative form even though it’s a direct object?

In Russian, masculine inanimate nouns and their adjectives have the same form for nominative and accusative. Here дополнительный (masculine, singular) and чемодан (masculine, singular) remain unchanged in the accusative because the object is inanimate.

What does дополнительный mean, and how is it different from лишний?

дополнительный means “additional” or “extra” in a neutral/positive sense (something added deliberately).
лишний means “superfluous” or “unnecessary” (implying it’s more than needed).
So дополнительный чемодан is an extra suitcase you intentionally brought, whereas лишний чемодан would sound like an unwanted or needless bag.

Can I change the word order, for example put я at the beginning?

Yes. Russian word order is quite flexible for emphasis. You could say:

Я взял дополнительный чемодан для поездки.
Дополнительный чемодан я взял для поездки.
Each ordering shifts the focus slightly but the basic meaning stays the same.

Where is the stress in дополнительный, and how do I pronounce it?

The stress falls on the third и: дополни́тельный.
Pronunciation guide: da-po-NEE-tel-ny (with the main stress on “NEE”).