That will be up to you to decide with odor, flavor and texture being determining factors. How good it is will depend a lot upon under what conditions it has been stored. But the best flavor will have gone by.
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The date on the mayonnaise is likely not an expiration, but a "best by" date. The concern would not be food safety, but food quality - since the pH of commercially prepared mayo should not support the growth of pathogens, but the fats could be rancid. If the jar is still properly sealed and just a few days beyond the date, you could open it and give it a sniff test. How well it has kept depends upon several things, including storage conditions (heat, exposure to light, etc.)
Whether or not you use it is up to you. Mayo isn't all that expensive and you wouldn't want rancid mayo to ruin your recipe.