Learn Hardcore Chinese: wǒ juéde jìzhù zhèxiē shēngcí bù róngyì. - I think it is not easy to memorize these new words.

Both are grammatically correct.
The version without 是 is more neutral and conversational; with 是 … 的 sounds a bit more deliberate or emphatic.

Why is there no 很 before 容易? I learned that Chinese often uses 很 before adjectives.

You’re right that very often we see:

今天很冷。 – “Today (is) cold.”

Here, 很 can be just a “linker,” not strongly meaning “very.”

But when the adjective is negated with 不, we normally don’t add this dummy 很:

不容易 – “not easy”
不方便 – “not convenient”
不贵 – “not expensive”

So 记住这些生词不容易 is the natural pattern here.

If you say 很不容易, you’re really emphasizing:

很不容易 ≈ “really not easy / pretty hard / very tough”

So:

不容易 – neutral “not easy”
很不容易 – strong emphasis “really not easy”

What is the difference between 觉得, 想, and 认为?

All three can translate as “think” in English, but they’re used differently.

觉得: “to feel / to have the impression that”
- Used for opinions, feelings, subjective judgments.
- Very common and neutral in speech.
- 我觉得这本书不错。 – “I think this book is good.”
想: has several meanings:
1. “to think, to consider”
  - More about the mental activity, not so much a judgment.
  - 我在想明天做什么。 – “I’m thinking about what to do tomorrow.”
2. “to want”
  - 我想喝水。 – “I want to drink water.”
3. “to miss (someone)”
  - 我很想你。 – “I miss you a lot.”
认为: “to consider, to hold the opinion that”
- More formal and used in serious statements or written language.
- 很多专家认为这个办法最好。 – “Many experts think this method is best.”

In this sentence, we want a personal feeling/judgment, so 觉得 is the natural choice:

我觉得记住这些生词不容易。
“I feel/think (that) memorizing these new words is not easy.”

What is the difference between 记, 记住, and 记得?

All relate to “remember / memorize,” but they focus on different aspects:

记 – the base verb “to remember / to write down / to record”
- 记笔记 – “to take notes”
- 我记你的号码。 – “I’ll write down / remember your number.” (context decides)
记住 – remember and have it stick; emphasizes achieving a result and keeping it
- Verb + 住 (result complement) = “to successfully keep in mind”
- 你一定要记住他的名字。
  “You must remember his name (and not forget it).”
- 记住这些生词不容易。
  “It’s not easy to memorize these new words (so they stay in your memory).”
记得 – “to remember (now)”; focus on the state of remembering
- 你还记得我吗？ – “Do you still remember me?”
- 我不记得他的名字了。 – “I don’t remember his name anymore.”

So in this sentence, 记住 is used because we’re talking about the effort of memorizing and making the words stick in your memory.

What exactly does the 住 in 记住 do grammatically?

住 here is a result complement. It indicates the result or outcome of an action: “to stay, to be fixed in place.”

Common patterns:

V + 住: “do V and make it stay / keep it”
- 记住 – remember (and keep it in memory)
- 留住 – keep (someone/something from leaving)
- 抓住 – grab and hold onto
- 记不住 – “cannot memorize (it won’t stay in my memory)”

So 记住 literally feels like “remember-and-hold-it” rather than just “touch it with your memory once.”

Why can 这些 go directly before 生词 without a measure word?

In standard grammar, numbers and demonstratives usually need a measure word:

三本书 – three books
这本书 – this book

But 些 (xiē) itself functions as a kind of plural/quantity word meaning “some / these / those (plural).” So:

这些生词 – “these new words”
那些人 – “those people”

You do not need an extra measure word between 这些 and 生词.

You could say 这几个生词 (“these few new words”) if you specifically mean a small number, but that’s a different expression.

What’s the difference between 生词 and 新词?

Both literally contain the idea of “new word,” but they’re used differently:

生词: “new/unknown vocabulary (for the learner)”
- Words that you personally don’t know yet.
- Often used in textbooks and classrooms.
- 今天我们学习十个生词。 – “Today we’ll learn ten new vocabulary words.”
新词: “new word” in the sense of recently created or newly coined in the language
- Like slang, buzzwords, technical neologisms.
- 最近出现了很多网络新词。 – “Recently, many new internet words have appeared.”

In your sentence, we’re talking about vocabulary that the speaker finds new/unknown, so 生词 is correct.

Why is 不 used here and not 没?

不 and 没 both negate, but they are used differently:

不:
- Used mainly with adjectives and habitual / general actions.
- 不容易, 不贵, 不高兴 – “not easy, not expensive, not happy”
- 我不去。 – “I’m not going / I don’t go.”
没:
- Mainly used with past or completed actions and existence/possession.
- 我没去。 – “I didn’t go.”
- 我没钱。 – “I don’t have money.”

Here, 容易 is an adjective (“easy”), so we use 不:

不容易 – “not easy”

没容易 is not used.

Could I say 我觉得记住这些生词很难 instead of 不容易? What’s the difference?

Yes, 我觉得记住这些生词很难。 is perfectly correct and natural.

Nuance:

不容易 – “not easy”
- Slightly softer; can sound a bit more neutral or less blunt.
很难 – “very difficult / quite hard”
- Feels a bit stronger and more direct.

So:

我觉得记住这些生词不容易。
“I think it’s not easy to memorize these words.” (fairly neutral)
我觉得记住这些生词很难。
“I think it’s (quite) hard to memorize these words.” (more clearly “hard”)

In many contexts they can be used interchangeably, but 很难 tends to sound a bit stronger.

Is 我觉得记住这些生词很不容易 correct? How is it different?

Yes, 我觉得记住这些生词很不容易。 is correct.

很不容易 intensifies 不容易, so it means something like:
- “really not easy”
- “pretty tough”
- “quite difficult”

Rough comparison:

不容易 – “not easy”
很不容易 – “really not easy / very hard”
很难 – “very difficult”

So 很不容易 expresses both negation (不) and strong degree (很), and it often carries a nuance of effort or struggle, especially in longer narratives:

走到这一步很不容易。 – “It was really not easy to get to this point.”