Learn Hardcore Korean: sukjereul haeseo chinguwa norayo. - I do my homework and then play with my friends.

Sequence (“do A and then do B”) as in 숙제를 해서 친구와 놀아요 (“I finish homework and then play with my friend”).
Reason or cause (“because A, B happens”), e.g. 배가 고파서 밥을 먹었어요 (“I was hungry, so I ate”).

Here, it shows you complete the first action before moving on to the second.

How is -아서/어서 different from -고 when linking verbs?

Both -아서/어서 and -고 connect actions, but:

-고 is a neutral listing connector: “A and B” without implying cause or sequence strongly.
Example: 책을 읽고 텔레비전을 봐요 (“I read a book and watch TV”).
-아서/어서 emphasizes that A is a prerequisite or direct cause/sequence of B.
In 숙제를 해서 친구와 놀아요, doing homework is necessary before playing.

Why is 친구와 used instead of 친구랑, and can I use 친구랑 here?

Both -와/과 and -랑/이랑 mean “with,” but differ in formality:

-와/과 is slightly more formal or written.
-랑/이랑 is colloquial and very common in speech.

You can say 숙제를 해서 친구랑 놀아요 in everyday conversation without changing the meaning.

Why is there no subject like “I” in this sentence?

Korean often omits the subject when it’s clear from context. The listener infers that I (저 or 나) is the subject. Including it is possible but usually unnecessary:

(저가) 숙제를 해서 친구와 놀아요
This is correct but more formal or emphatic.

Why is the verb 놀다 conjugated as 놀아요?

놀다 (“to play”) is a verb ending in a vowel stem (ㄹ). In the polite present tense:

Drop 다 → 놀-
Add -아요 → 놀아요
This is the standard polite style you’ll use with strangers or acquaintances.

Why is 숙제 followed by -를 in 숙제를 해서?

-를/을 marks the direct object of a verb. Since 숙제 (“homework”) is what you’re doing:

Vowel-ending noun + -를 → 숙제
- -를 = 숙제를
  This tells us “homework” is the thing being done.

Can I express this sentence in the past tense?

Yes. Change both verbs to past polite forms:

하다 → 했어요
놀다 → 놀았어요
So you get: 숙제를 해서 친구와 놀았어요 (“I did my homework and played with my friend”).