You explain it in the same way as here - truthfully and in honest and straightforward language.
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Be truthful on the application and at the interview. While there is a general prohibition to adjusting status if you have worked illegally in the US, there is an exception if you are adjusting based on marriage to a US citizen. No additional forms are needed. There is no penalty unless you used fake documents to work.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
Just be truthful and disclose all your previous unauthorized employment. I have good news for you: spouses of US citizens can never be penalized for any on authorized employments, due to the fact that they are deemed as "immediate relatives" (IRs). The law as it stands does not allow USCIS is to penalize IRs for any previous unauthorized employment. Rest assured.
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