Take one of these books if you like.
Take one of these books if you would like.
What is the difference in meaning ? And is it standard to say would like after if ? I think in standard English after if we put only the verb not would + verb.
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In the situation you describe, there is no difference or preferred way. However, if you were to say
Would you like one of these books?
That has a different meaning than
Do you like one of these books?
In the first example, there is an implication of receiving a book, like
Would you like to have one of these books?
However, in the second one, the context is more about the word like as in enjoy.
However, in the particular phrasing you give, there is, again, no difference. It could be argued that would is implied in the first sentence. Although neither is preferred (grammatically), you will most likely hear the first one more just because it's shorter.
In this context, would has this meaning in the Oxford Dictionary:
- Expressing a polite request:
Would you pour the wine, please?
The second form is just a slightly more polite form of the first, along the same lines as
Would you like a glass of wine?