Would" is used to express a polite request, while "may" is used for permission, "can" is used for ability, and "should" is used for advice or recommendations.

Modal Auxiliaries and Polite Requests

Modal auxiliaries are a class of verbs that are used to express various meanings such as ability, possibility, necessity, permission, and more. They are often used to modify the main verb in a sentence and add additional information or nuances to the statement. One common use of modal auxiliaries is to express polite requests.

Polite Requests
Polite requests are a way of asking for something or seeking assistance in a courteous and respectful manner. They are commonly used in social interactions, formal situations, or when addressing someone with authority. Politeness is often conveyed through the use of certain modal auxiliaries.

Modal Auxiliary "Would"
The modal auxiliary "would" is commonly used to express a polite request. It is used to make a request in a more indirect and courteous manner. When using "would" to make a request, the sentence structure usually follows this pattern:
Subject + modal auxiliary "would" + base form of the verb + object.

Examples:
1. Would you please pass me the salt?
2. Would you mind closing the window?
3. Would you be able to help me with this problem?

In these examples, "would" is used to soften the request and make it more polite. It conveys a sense of courtesy and respect towards the person being addressed.

Other Modal Auxiliaries
While "would" is the most commonly used modal auxiliary to express polite requests, other modal auxiliaries can also be used depending on the context and level of formality. Here are a few examples:

- "May": May I please borrow your pen?
- "Can": Can you please lend me a hand?
- "Could": Could you possibly pick up some groceries for me?
- "Will": Will you kindly turn off the lights?

These modal auxiliaries can also be used to make polite requests, but "would" is generally considered the most appropriate and commonly used auxiliary in this context.

In Conclusion
The modal auxiliary "would" is used to express a polite request. It is frequently used in social interactions and formal situations to convey a courteous and respectful tone. While other modal auxiliaries can also be used to make polite requests, "would" is the most commonly used and accepted option.