Learn Hardcore Korean: jigeum sukjereul pulgo isseoyo.

풀다 means “to solve” (as in solving problems or exercises). It’s a transitive verb, so you attach an object particle like -을/를 to the thing being solved (e.g. 숙제를 풀다 = “to solve homework”).

Why is the verb form 풀고 있어요 used instead of just 풀어요?

풀어요 is the simple present (“I solve” or “I will solve”), whereas 풀고 있어요 is the present progressive (“I am solving”), emphasizing that the action is ongoing right now.

What exactly does the ending -고 있어요 indicate?

The pattern verb stem + -고 있다 expresses the progressive aspect (an action in progress). In polite speech, 있다 becomes 있어요, so 풀고 있어요 literally means “am/are/is solving.”

What is 숙제를, and why is -를 attached to 숙제?

숙제 means “homework.” The particle -를 marks 숙제 as the direct object of the verb 풀다. Without -를, the sentence wouldn’t clearly show what is being solved.

What does 지금 mean, and where can I place it in the sentence?

지금 means “now.” It’s a time adverb, so you can put it at the very beginning (지금 숙제를 풀고 있어요) or right before the verb (숙제를 지금 풀고 있어요), though most learners start with it at the front.

Why is 있어요 used here? Is it the main verb “to exist”?

In -고 있어요, 있어요 is an auxiliary verb showing continuous aspect, not the main verb “to exist.” It helps form the progressive tense with -고.

How can I make this more formal, more casual, or turn it into the past progressive?

• More formal polite: 지금 숙제를 풀고 있습니다
• Casual (to friends): 지금 숙제 풀고 있어 or simply 숙제 풀고 있어
• Past progressive: 지금 숙제를 풀고 있었어요 (“I was solving my homework just now.”)