So I starting playing D&D recently and I am playing through the Lost Mine of Phandelver. I am playing with my brothers, and we have a decent amount of tabletop RPG experience, but only one of the three will RP their characters, and it's so FRUSTRATING! Does anybody have tips on how to get them to roleplay more?

There was a twitter thread a while ago started by D&D beyond's account asking what everyone's favorite house rules are. One of the replies was that they give advantage on the skill or ability check needed for something if the player acts out or describes in detail what they want to do prior to the DM declaring what roll is needed. I got into a brief conversation with that DM who said that he has found it very helpful in encouraging new players to explore RP. That new players (and maybe this is something your brothers are feeling despite their prior RP experiences) are 1- anxious about RP and 2- afraid of disappointing everyone at the table by failing. Giving advantage helps them succeed which in turn helps them overcome that anxiety so maybe they won't be afraid to try their wild and crazy ideas. Also helps by rewarding RP. I'm trying it with the group I DM (which is my brother and two of his kids) since they're new and inexperienced (or rusty in my brother's case) with both ttrpgs and rp in general.

its not up to you to decide they need to RP more. some players just dont want to. Meaning as a DM you either accept that or find another group that is more in line with the kind of game you want to run.

Quote from Giblix >>

its not up to you to decide they need to RP more. some players just dont want to. Meaning as a DM you either accept that or find another group that is more in line with the kind of game you want to run.

I really don't think that's a good approach to the issue. Usually, the lack of RPing is due to some fears and/or lack of skills to do that, so helping players to unlock it is a part of DMs job. Maybe some of them don't feel comfortable or are shy and that's ok, but in the span of the whole campaign, it's good to work on it with players - mostly because they will definitely have more fun role-playing. Now, RP doesn't mean they have to do perfect new voices or anything like that, but actually going through the game as a character is a core of TTRPG. 

In my case, I started with baby steps with my group. One of the things were - when they wanted to use an ability they would tell me what they want to roll e.g. 'I want to roll survival to check the tracks". My rule is, you don't say what you roll, you tell me what you want to do and I decide what you roll. Changing this one thing turn their whole perspective on roleplaying their abilities. They would start with describing things they try to do - I would make them roll for appropriate ability and base on how they RP and dice, give the final results. 
This one little change opened them up for more exploration with the characters by role-playing them more and they definitely have more fun today. 

It all depends what you mean by "role play".

If you mean make in-game decisions based on their characters' abilities, knowledge, goals, and personality - then yes, they do need to be doing that.

If you mean talk in character, and generally "act", then no - they don't need to do that. That's an aspect that people either like doing, or they don't like doing, and I'm of the opinion that you shouldn't force it ( and you can't anyway - all you'll do is put your Player on the spot and make them unhappy ). While I do very much like Critical Role - I think it has done a disservice to new Players and DMs by setting that level of character acting as the expected baseline. It's not.

You absolutely cannot force someone to play in a particular style. The best you can do is make it easy, "safe",  and fun to play in a particular style, and leave it up to them if they want to bite, or not.

You can absolutely - as suggested - do things to facilitate Player role-playing however ( RP of either definition ).

• Ask them to frame actions in terms of what they want to do, and what it is intended to accomplish - not based on what Skill score they want to roll against ( as  Nathirwalowsku suggested ).
• Lead by example - have all your NPCs speak in character. Basically, you do the acting, don't pressure them to be actors, but create an environment where it's allowed, and demonstratively fun to do so. Maybe some of them will come around - but if they don't ever come around, that's OK.
• Disallow actions or choices that utilize out-of-character knowledge: " Would you know that? ", " Would you know how to do that? ", " You're an Int 3 fighter, would you really know to avoid those arcane symbols? ".
• Have the world respond to the characters as they are being played, not how they are on paper. That Bard is written as a really nice, personalble, and pleasant character, but the Player plays them as a dick? The world assumes they are a dick. Essentially however they play them is the role-playing; they're just re-defining the role.

If, however, at the end of the day, you want to play with a group that plays in a particular style, and they want to play in a game of a different style, you have a group/DM disconnect. You might be able to negotiate a style of game that works for everyone imperfectly, but in some cases you just can't make a group fit together.

That doesn't make either side wrong - it just makes them incompatible. Nothing wrong with that, but if that's the case, you're better off just playing with different people.

A lot of what has been said I agree with almost completely. RP/Acting is something that is learned, fostered, and grown. RP/Acting is hard, embarrassing and makes people feel vulnerable if they're not used to it.

I have a game that is almost 3 years old now and when it comes to RP, my players are all over the board. Two of my players are very much willing to get into character, talking, acting, speaking, even dressing like their characters if they can pull it off. Two of my players fluctuate between in character and third person all through the night. My last player almost never leaves the 3rd person. None of them takes away from the game in any way, they all add their personality and gaming style, which gives us the ability to enjoy our nights. 

When I DM, and when I play, I am very outgoing and get into my roles. I take on voices, physical tics, and describe things in detail. I really get into my role play and I have no problems doing it. By acting this way I enjoy myself, and often I get the table into it as well, they have very real reactions to the voices and descriptions I give them. The thing is, I don't expect it from my players, I understand that not everyone is going to fit into that mold. I open the door for my table to be able to act that way, I'd love to have everyone at my table be as outgoing, I'd love to have each of them "become" their characters, but I know that isn't going to happen all the time. 

In the end it's up to you to figure out how to give your players what they enjoy at the table while still doing what you enjoy.

thank you all for your suggestions! this has already helped in terms of the mindset I should have when dealing with this problem.

Also reward your players who do well at it. The inspiration system is great for that. Even your shy/timid players who are not great at role playing, if they show a little effort, give them some inspiration; especially if they do something that makes their character suffer in some way [jumping on a grenade for the team].

Perhaps it's a totally different topic - but how often does Inspiration actually get used? 

A reward that they don't value, isn't really a reward.

I totally agree that rewarding behavior you want to encourage is a means of getting more of that behavior; I'm just not convinced that Inspiration is the way to go.

I think small XP bonuses might work best - although "giving XP for role-playing" has become a sneer-able point in some circles ( I think this against the idea of giving out XP for character acting, not necessarily character development ). 

My players use it whenever they can! It can really help in times they roll terribly. I give them the option to turn a critical fail into a regular fail. I do not give out inspiration all the time as I want them to value it as much as possible.

I very much like your use of it to offset a critical failure.

What you are really giving out is a limit use Luck Point - but I agree that's much more likely to be used.