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This is a Crabgrass (Digitaria spp.), and judging from the size and general appearance of the plant, it is most likely Hairy Crabgrass (Digitaria sanguinalis), also known as Large Crabgrass.
For a more definite species determination it would be best to see close up images of the leaves, as well as the spikelets when they are produced.
Digitaria is in the Panicgrass tribe (Paniceae) of the Grass Family (Poaceae). Digitaria sanguinalis originated somewhere in Eurasia or North Africa but is now a widespread warm-season annual weed in lawns and ruderal areas.
Cheatgrass (Bromus tectorum), or Downy Brome, is a very different annual grass in the Brome trime (Bromeae) of the Grass family (Poaceae). it is smaller in stature and shorter-lived, often going from germination to flowering in only a couple months. It could appear as a lawn weed, but is usually ,more prevalent in drier landscapes. Once you become familiar with Cheatgrass you are unlikely to ever mistake it for a crabgrass.