Contracted and uncontracted negative questions have different word order.

Compare: 

Won’t you come? (contracted negative question)

Will you not come? (uncontracted negative question)

Don’t you understand? (contracted)

Do you not understand? (uncontracted)

Note that uncontracted negative questions are rather formal. In an informal style, we use contracted forms.

Uses of negative questions

Negative questions are often used to express opinions in a more polite way.

Wouldn’t it be better to put the heating on? (More polite than ‘It would be better to put the heating on.’)

Negative questions are also used in exclamations.

Isn’t she a lovely girl!

In polite requests, invitations, offers, complaints etc

Pressing invitations and offers often begin with ‘Won’t you…?’ ‘Wouldn’t you…?’ or ‘Why don’t you…?’

Why don’t you come and have dinner with us?

Wouldn’t you like something to drink?

‘Won’t you like to spend the weekend with us?’

Grammar notes

We do not normally use negative questions to ask people to do things. Instead, we use ordinary questions. Note that negative questions may be understood as complaints or criticisms.

Compare:

Can you help me for a moment? (polite request)

Can’t you help me for a moment? (criticism meaning something like ‘Are you so unkind that you can’t help me for a moment?’)