Grammaticality – How to Drive into Town When You Can’t Drive

"Drive safely" is the formally correct phrase.

Saying "drive safe" sounds casual and informal; however, many people do it. This is because, in general, people sometimes use the adjective form as an adverb (usually this means not adding -ly) in casual speech. It is not recommended in any formal situations.

"Do good" is a different kind of issue, because the form depends on the meaning you want to convey.

• If "do good" means "do the right/good thing", then "do good" is the formally correct phrase.

• If "do good" means "perform correctly/at a high level", then "do well" is the formally correct phrase. (But, as mentioned above, casually you could also say "do good" here.)

In the sentences:

After we've seen your performance, you will have shown us your talent.

After we've seen your performance, you will show us your talent.

the first sentence implies that the "showing of talent" takes place as part of the performance. The second implies that it will happen after the performance. So the meanings are different.