Learn French: Nous progresserons beaucoup dans ce domaine difficile. - We will progress a lot in this difficult field.

Progresser is a regular -er verb. To make it future tense, we just take the full infinitive (progresser) and add the future ending for nous, which is -ons. So, progresser + ons = progresserons.

Why is beaucoup placed right after the verb instead of at the end of the sentence?

When a verb is conjugated in a simple tense like the future tense here, adverbs of quantity like beaucoup (a lot) usually go immediately after the verb. It sounds unnatural in French to stick it at the very end of the phrase.

Can domaine also mean a physical "domain" or "estate"?

Yes! It often refers to a physical estate or piece of land (like a wine estate). But just like in English, it is frequently used figuratively to mean an area of knowledge, work, or study, which is why it translates well to "field" in this context.

Why does difficile come after the noun domaine?

In French, most adjectives go after the noun they describe. Only a specific group of short, common adjectives (usually describing Beauty, Age, Goodness, or Size) go before the noun. Difficile doesn't fit into that group, so it follows the normal rule.