Learn Hardcore Japanese: nooto no matigai wo kesigomu de kesite kudasai. - Please erase the mistakes in the notebook with an eraser.

Because の is the genitive/possessive particle linking two nouns. It shows that the mistakes belong to the notebook – literally “the notebook’s mistakes.”

Why is 間違い followed by を?

The particle を marks the direct object of the verb. Here 間違いを indicates “the mistakes” are what you are erasing.

Why is 消しゴム followed by で instead of を?

で marks the means or instrument used to perform an action. 消しゴムで means “with an eraser.” You wouldn’t say 消しゴムを because you’re not erasing the eraser itself.

What does the て-form 消して do before ください?

The て-form plus ください forms a polite request. 消してください literally means “please erase.” You always need the て-form of the verb when using ください to ask someone to do something.

Why is there no subject like you at the start of the sentence?

Japanese often omits the subject when it’s clear from context. In this request, it’s understood that you (the listener) are being asked to erase the mistakes, so there’s no need to explicitly say you.

Why is 消しゴム written partly in kanji and partly in katakana?

消し is the kanji for “erase/erasing,” a native Japanese element, while ゴム is a loanword (gairaigo) for “rubber,” so it’s in katakana. Many compound words mix scripts to reflect native roots and borrowed terms.

Could I drop ノートの and just say 間違いを消してください?

Yes—if the context already makes clear which mistakes you mean, you can omit ノートの. But including it clarifies which mistakes to erase.

What’s the difference between 消してくれ and 消してください?

消してくれ is a rough, casual imperative (“erase it for me”) used among close friends or to subordinates. 消してください is the polite form, suitable in formal situations or when showing respect.