How to *multiply* (for lack of a better term) two dataframes

Question

I have 2 simple dataframes defined by:

persons = pd.DataFrame({
    'name': ['Alice', 'Bob']
})

and:

periods = pd.DataFrame({
    'year': [2019,2019,2020,2020],
    'semester': ['s1', 's2', 's1', 's2']
})

How can I multiply (for a lack of a better term) the two dataframes so the result would be:

result = pd.DataFrame({
    'name': ['Alice', 'Alice', 'Alice', 'Alice', 'Bob', 'Bob', 'Bob', 'Bob'],
    'year': [2019,2019,2020,2020,2019,2019,2020,2020],
    'semester': ['s1', 's2', 's1', 's2', 's1', 's2', 's1', 's2']
})