Learn Hardcore Polish: Ona umie kroić warzywa szybciej niż ja. - She knows how to cut vegetables faster than I do.

"Potrafi" also means "is able to/can," often sounding a bit more neutral/formal and can emphasize being capable of achieving a result.
"Może" means "may/can" in the sense of permission or possibility, not learned skill.

Examples:

Bold Polish shows the pattern, English explains.
Ona umie kroić warzywa. = She knows how to cut vegetables.
Ona potrafi pokroić warzywa w pięć minut. = She is capable of cutting the vegetables in five minutes.
Ona może kroić warzywa teraz. = She may/is allowed to cut the vegetables now.

Can I drop "Ona"?

Yes. Polish often drops subject pronouns when context makes them clear. Umie kroić warzywa szybciej niż ja is grammatical, but 3rd person present forms don’t show gender, so Ona clarifies that it’s “she” (not “he”). Keep Ona if you need clarity or emphasis.

Why is it "kroić" and not "pokroić"?

Kroić (imperfective) focuses on the process/habit/skill: knowing how to cut in general. That fits comparisons of manner like “faster.”
Pokroić (perfective) focuses on completing the action: cutting something up to a finished result. With “speed,” imperfective is the default: Ona umie kroić warzywa szybciej niż ja. You can say Ona potrafi pokroić warzywa szybciej niż ja to stress finishing in less time, but it subtly shifts the focus from manner to time-to-completion. Both are understood.

What’s the difference between "kroić," "ciąć," "siekać," and "szatkować"?

kroić = cut/slice into pieces (typical kitchen “cutting” with a knife; neutral).
ciąć = to cut in general (rope, paper, prices), not specifically food prep.
siekać = to chop finely (e.g., onions, herbs).
szatkować = to shred/slice thinly (e.g., cabbage). Perfective partners: pokroić, pociąć, posiekać, poszatkować.

What case is "warzywa" and why? Would it change under negation?

After a transitive verb like kroić, the object is in the accusative. Warzywa here is accusative plural (it looks the same as nominative plural for neuter nouns). Under negation, Polish usually switches to genitive:

On kroi warzywa. = He is cutting vegetables. (acc.)
On nie kroi warzyw. = He is not cutting vegetables. (gen.)

Should it be "szybciej niż ja," "szybciej ode mnie," or "szybciej niż mnie"?

szybciej niż ja is standard; after niż (than) use nominative because it’s like “than I [do].”
szybciej ode mnie is also fully standard; with od use genitive (mnie). The form ode is for euphony before certain words.
szybciej niż mnie is common in speech but considered less formal/standard.

Can I use "jak" instead of "niż"?

Not for inequality. Use:

szybciej niż… = faster than…
tak szybko jak… = as fast as… (equality)

Can I move "szybciej" to other positions? What word orders are natural?

Yes; common options:

Ona umie kroić warzywa szybciej niż ja. (neutral)
Ona umie szybciej kroić warzywa niż ja. (also fine)
Umie kroić warzywa szybciej niż ja. (dropping the pronoun) You can also drop “umie” and state a fact/habit: Ona kroi warzywa szybciej niż ja (she cuts faster than I do), but that shifts the meaning from “ability” to “actual performance.” Avoid odd orders like placing the whole “szybciej niż ja” chunk at the start unless for special emphasis.

How do you conjugate "umieć"?

Present:

ja umiem
ty umiesz
on/ona/ono umie
my umiemy
wy umiecie
oni/one umieją Past (examples): on umiał, ona umiała, oni umieli, one umiały. Future is periphrastic: będzie umiał/umiała
- infinitive. Avoid the nonstandard form “umią.”

How do I pronounce the tricky parts (ć, ż, j, "szy")?

Approximate hints:

ć in kroić = “ch” in “cheek,” but softer: kro-yeech.
ż in warzywa/niż = “zh” in “measure”: va-ZHI-va, neezh.
j in ja = “y” in “yes”: ya.
szy in szybciej ≈ “shih”: SHI-b-chay (the “ciej” is like “chay”). Polish stress is usually on the second-to-last syllable: o-NA, U-mie, KRO-ić, war-ZY-wa, SZYB-ciej.

Are there articles in Polish? How would I say “the vegetables”?

Polish has no articles. Context does the job. If you need to specify, use a demonstrative:

te warzywa = these/the vegetables (ones near/known)
tamte warzywa = those vegetables

Could I use "potrafi" here instead of "umie"?

Yes: Ona potrafi kroić warzywa szybciej niż ja. It’s natural. “Potrafi” can sound a bit more about capability/competence, while “umie” is the everyday “knows how to.” In most contexts they’re interchangeable.

Why "szybciej" and not "bardziej szybko"?

Many adverbs have their own comparative form in -ej. Use szybko → szybciej, not “bardziej szybko.” Use “bardziej” for words that don’t form comparatives themselves (e.g., ostrożnie → bardziej ostrożnie).

Should it be "szybciej" (adverb) or "szybsza/szybszy" (adjective)?

Use the adverb szybciej to modify a verb (how she cuts): Ona kroi szybciej niż ja. Use the adjective szybsza/szybszy with a noun or after “to be”: Ona jest szybsza niż ja.

Does "umie" always take an infinitive? Is the pattern the same with other skills?

Yes, the common pattern is umie/potrafi + infinitive:

Umiem gotować. = I know how to cook.
On potrafi pływać. = He can swim.
Ona umie kroić warzywa. = She knows how to cut vegetables.

Can I say “than me” in Polish, like "niż mnie"? And how do I add the tool, like “with a knife”?

“Than me” as niż mnie is widespread in speech but less formal; niż ja or ode mnie are the safest standard choices.
To add the tool, use the instrumental: kroić nożem = cut with a knife. Example: Ona umie kroić warzywa nożem szybciej niż ja.

Could I use "zna" or "wie" instead of "umie" to mean “knows how”?

No.

zna = knows (is familiar with) a thing/person/language: Zna ten przepis. (She knows this recipe.)
wie = knows a fact: Wie, że to trudne. (She knows that it’s hard.) For skills, use umie or potrafi: Ona umie kroić warzywa.