Learn Polish: Chodzę pieszo, a mój brat jeździ samochodem.

In English, we can say "I go on foot and he goes by car," using the same verb. Polish strictly separates going on foot (chodzić) from going by a vehicle (jeździć). Since the speaker is walking but the brother is driving, two completely different verbs are required!

Doesn't chodzę already mean "I walk"? Why add pieszo?

Yes, chodzę implies moving on foot, but it can also just mean "I go (regularly)" to a place, like school or work. Adding pieszo (on foot) specifically emphasizes the method of travel, making a direct contrast with the brother's method of using a car.

Why is the word "a" used here instead of "i" (and) or "ale" (but)?

The word a is a contrasting conjunction. It is used to compare two different situations or subjects, similar to "whereas" or "while" in English. Here, it sets up the contrast between how you travel and how your brother travels. Using i would just be a flat list of facts, while ale would imply a stronger, unexpected contradiction.

Why is the word for car (samochód) spelled samochodem here?

When you talk about the means of transportation you use, Polish requires a grammatical form called the Instrumental case. For most masculine nouns ending in a consonant, like samochód, you change the ó to a regular o and add -em to the end. That is why "by car" becomes the single word samochodem.