That is due to some insect on the palms. The most likely culprits are scale or mealybugs. Check the leaves closely for these insects. Scale appear as small flat objects perhaps the size of a typed letter "o". Mealybugs are white and cottony/waxy in appearance. Your local garden center can provide an appropriate product for whichever you find. Just make sure it is labeled for use on palms and then move the plant outdoors to a very shady area for treatment and recovery. It may take 2 or 3 applications over a 4 week period to get good control and complete coverage with the spray is critical.
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