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I accept payment in the forms of cash and credit.

OR

I accept payment in cash and credit.

Are these sentences both correct?
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I accept payment in the form of cash or credit card.

I accept payment in cash or by credit card.
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Is there a way to express both?

Like both cash and credit card?
What I gave you expresses both. Obviously any one customer will use only one of the two options. However, you can also say 'We accept both cash and credit cards'.