The first thing you need to ensure is that the polishing compound you have chosen is not too abrasive. You can do this by applying the car wax on a car part which is not so much visible such as inside the trunk or under the hood.
If the polishing compound that you are using is too abrasive, chances are that you will end up damaging the paint on and around the scratched area.
Apply a uniform layer of the polishing compound to the scratch using the sponge. Make sure that you do not use too much polishing compound. Start scrubbing the area to which you applied the polish in circular motion. Keep scrubbing with a soft hand until the scratch is no longer visible.
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Now you have to apply the car wax. Take another sponge and apply the liquid car wax to it. Use to this sponge to buff the area in a circular motion. Continue to buff until the shine returns and becomes uniform with the rest of the paint.
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To remove the excess liquid wax, you need to use a soft clean towel. Carefully buff off the excess wax. Make sure that the towel is clean and does not have any dirt particles trapped in it because if you buff the area with a dirty towel, chances are that you will end up with more scratches than before.