Learn Russian: Я режу этот хлеб своим новым ножом. - I am cutting this bread with my new knife.

In Russian, the tool or instrument you use to do an action (like cutting with a knife) is put into the instrumental case. Notice that we don't need a preposition for 'with' here; the case endings on своим новым ножом do that job for us.

Why does the sentence use своим instead of моим for 'my'?

Свой is a reflexive possessive pronoun that means 'one's own'. You use it when the owner of the object is also the subject of the sentence. Since я (I) is the subject doing the cutting, you use своим (my own) rather than моим. While моим wouldn't be grammatically wrong, native speakers strongly prefer своим in this situation.

How do the endings for своим новым work in the instrumental case?

Masculine adjectives in the instrumental case generally take the ending -ым (or -им after certain letters), which gives us новым. Possessive pronouns like свой take the ending -им, making it своим. Both of these agree with the masculine instrumental noun ножом.

The verb is режу. What is the infinitive, and why is there a ж instead of a з?