Okay, I’ve been seeing this one a lot lately, and it’s really starting to get to me.
People: “Would of” is not a thing. Don’t type that.
The correct phrasing is “would have.” The contraction is “would’ve” and when you say it out lot, it does sound a little like “would of,” but that’s so, so wrong. And it makes me think that you are incredibly stupid because when you type “would of” instead of one of the proper forms, technically, your sentence no longer means anything. Or, it means something that doesn’t make any sense.
See, “have” and “of” have very different meanings. “Have” is possessive in favour of the subject, most often describing a missed opportunity of some description. “Of” in this case, would make it to mean that the “would” belongs to the object. See the following improper sentence:
Paul would of eaten the cake.
You can sort of make this sentence meaningful by adding a comma, turning “would” into a title, and making “eaten the cake” the name of a place.
Paul, Would of Eatenthecake.
And now it’s stupid. See what you did? Stop being stupid! Write it this way:
Paul would have eaten the cake.
Or this way:
Paul would’ve eaten the cake.
And it will be correct. And you will no longer be stupid. I feel like I shouldn’t have to add this, but the same rule goes for “should have” and “could have.” Stop putting “of” where it doesn’t belong! ARGH!
Fun fact: The “would have [verb]” construction is, in the English language, known as the Conditional Perfect. This is mostly irrelevant to everything.