Auxiliary Verbs: can and could, will and would

 Hi...everybody! In this article, I write about auxiliaries. An auxiliary verb is a verb that gives further semantic or syntactic information about a main or full verb. It is also called helping verb, helper verb, or verbal auxiliary, and abbreviated AUX. It is suitable for students in grade 3-6 or more. So, I hope this article can help you. Let's check!

Auxiliary, or helping verbs, are used before infinitives to add a different meaning. For example, you use auxiliary verbs to say:

that someone is able to do something,

that someone is allowed to do something, or

that someone has to do something.

The hellping verbs are can, could, 

would, should, ought to, will, shall, may, might and must.

Can and Could
Use can and could to say that someone is able to do something.

She can draw really good pictures.
Philip can run faster than Matt.
Can you ride a bike?
Can you help me with my homework?
She could already read before she started school.
Our teacher said we could go home early.
I ran as fast as I could.
Sarah could not come to the party because she was ill.

You may also use can and could to say that someone is allowed to do
something.

My mom says you can come to our house for dinner.
Dad says I can’t walk to school on my own.
You can’t go in there without a ticket.
Mom said I could have ice cream after my dinner.
The big sign on the gate said PRIVATE, so we couldn’t go in.

Can and could are also used for asking for information or help, for
offering something, and for suggesting something.

Can you tell me if this train goes to Topeka?
Could you show me where the accident happened?
Could you open that window, please?
You can borrow my pen, if you like.
Your sister could come with us, if she wanted to.
I could lend you my football.
We can go to the library instead.
You could ask your dad to help us.
John can borrow his brother’s skates.

Will and Would
Use will and would when you are asking someone to do something.

Will you please stop making that noise?
Would you pass me that book, please?
Please, will you close the door? 
 
You can also use will and would to offer something or to suggest something.

Will I hold this end of the rope?

Will I carry the bag for you?

Would you like another drink?

Which cake would you like?

 taken from, BASIC ENGLISH GRAMMAR for english language grammar learners. Howard Sargeant.
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Reference: Wikipedia, usingenglish, grammar.about