Usage patterns
〈場所〉の田畑を耕すto till/cultivate the fields (of a place)
My grandfather tills the fields at home every morning.
田畑が広がるfor fields to stretch out (as scenery)
Fields stretch out around the village.
田畑を荒らすto ravage/damage fields (e.g. by animals, flooding)
Wild boars are ravaging the fields, which is a real problem.
田畑を持つto own farmland
Many households in the countryside own farmland.