Learn Hardcore Korean: geu munjeneun jeonhyeo eoryeopji anhayo.

Yes. 가 marks “that problem” as the grammatical subject and sounds like a neutral statement of fact. 는 is more topical/contrastive. Both are correct; choose based on nuance.

Do I need 그? What’s the difference among 이/그/저?

그 points to something known from context or near the listener (“that”).
이 is near the speaker (“this”), 저 is far from both (“that over there”).
You can drop 그 if context already makes the problem clear. Without it, 문제는… just means “the problem (we’re talking about)…”

What exactly does 전혀 mean, and where does it go?

전혀 means “completely/at all” and in standard Korean it pairs with a negative. It goes right before the negated predicate: 전혀 어렵지 않아요 or 전혀 안 어려워요. Don’t put it after the predicate.

Can I use 전혀 with a positive verb, like 전혀 쉬워요?

Not in standard usage. 전혀 sounds natural only with a negation. For positive emphasis, use 아주/매우 (“very”) or 완전히 (“completely”) depending on meaning.

What’s the difference between 어렵지 않어요 and 안 어려워요?

Both mean “not difficult.”

안
- adjective is short, casual, very common in speech.
-지 않다 is a verb ending; it can feel a bit more neutral/formal and is common in writing.
With 전혀, either works: 전혀 어렵지 않아요 ≈ 전혀 안 어려워요.

Why is it 어렵지, not 어려우지?

어렵다 is ㅂ‑irregular, but the ㅂ changes to 우/워 only before vowel-initial endings (e.g., 어려워요). Since -지 starts with a consonant, the ㅂ stays: 어렵 + 지.

How does 어렵지는 않아요 differ from 어렵지 않아요?

-지는 adds a contrastive nuance: “It’s not difficult (though it might be something else).” 어렵지 않아요 is a plain negation.

Any pronunciation tips for the whole sentence?

어렵지: the ㅈ becomes tense after the final ㅂ, so it sounds like [어렵찌].
않아요: the ㅎ usually drops; you’ll hear [아나요].
전혀: often reduced to [저녀] in fast speech; careful speech keeps [전혀].
Putting it together: roughly [그 문제는 전혀/저녀 어렵찌 아나요].

Is the spacing correct?

Yes: 전혀 어렵지 않아요. Write -지 않다 with a space: 어렵지 않아요 (not 어렵지않아요).

What politeness level is this? What are alternatives?

It’s informal polite (-아요/어요).

Formal polite: 어렵지 않습니다
Casual: 어렵지 않아 (or 안 어려워)
Plain/written dictionary form: 어렵지 않다

Can I drop the particle 는?

In casual speech you might hear 그 문제 전혀 어렵지 않아요. It’s understandable, but dropping particles can sound sloppy or ambiguous in careful speech or writing.

Is 문제는 ever pronounced or written as 문젠?

Yes, in casual speech 문제는 often contracts to 문젠. It’s fine in texting or dialogue; keep 문제는 in formal writing.

Are there other “at-all” words I can use instead of 전혀?

Yes, with negatives:

하나도: very colloquial “not at all” (e.g., 하나도 안 어려워요).
조금도: “not even a little.”
별로: “not particularly” (softer: 별로 어렵지 않아요).
거의: “hardly/almost not” (different nuance: 거의 어렵지 않아요).

Could I say this with the opposite adjective 쉽다?

Yes, but note the nuance:

전혀 어렵지 않아요 ≈ “It’s not difficult at all” → implies it’s easy.
전혀 쉽지 않아요 ≈ “It’s not easy at all” → implies it’s difficult.

Can I turn this into a question?

Yes:

Informal polite: 그 문제는 전혀 어렵지 않아요?
Casual: 그 문제 전혀 안 어려워?
Formal: 그 문제는 전혀 어렵지 않습니까?

Why is there no separate “to be” verb?

Korean descriptive words like 어렵다 function as verbs (descriptive verbs), so they serve as the predicate by themselves. You don’t need an extra “to be.”