Brushing too vigorously can eventually erode your gum tissue and tooth enamel, particularly if you're using a hard toothbrush. Look for a soft head and apply gentle pressure and circular motions when you clean—sawing back and forth is too harsh.
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And just FYI, you don't help your oral health by brushing longer, either. Never brush your teeth for more than two minutes, two or three times a day. And since frayed bristles can also injure your gums, always remember to replace your brush or brush head every three months.