Answer: The shade is probably contributing to your difficulty keeping the grass growing well. That's not unusual, though. Think of a dense woody area--often there is little growing underneath the trees in the shade, except maybe some ferns. I hesitate to recommend you do anything underneath the tree. Maples have lots of shallow roots, so you don't want to disturb that area too much. If you really want something growing under that tree, how about a shade-loving ground cover, like bugleweed (Ajuga) or lily-of-the-valley (Convallaria)? If you choose to try a ground cover--I would be very gentle when planting, and add no more than an inch or so of material to the ground underneath the tree. If you really want to improve the lawn, how about spreading a thin layer of compost or aged manure under the tree (again, no more than an inch deep) and re-seeding with a grass mix formulated specially for shade.
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