Which of the below sentences are correct?

a) The boy playing with the toy car is laughing loudly.
b) The boy playing with the toy car are laughing loudly.

Then why?

Which of the below sentences are correct?

a) The boy playing with the toy car is laughing loudly.
b) The boy playing with the toy car are laughing loudly.

Then why?

It's very simple: if the subject is single, the verb must also be single. That's what 'agreement' is all about.

So only a) is correct because it has a singular subject (boy) and a singular verb form (is). Example b) is wrong because it has a singular subject (boy), but a plural verb (are), so they don't match, or agree.

Another way to check the agreement in your examples is to omit the relative clause:

a) The boy is laughing loudly.
b) *The boy are laughing loudly.

It's clear now that only a) is correct.

PaulM