The difference between 胡乱 and 随便
随便 has several meanings. However, only one of the meanings is similar to 胡乱.
The same meaning
The adverbs 胡乱 
and 随便 emphasize that an action was done without much consideration.
and 随便 emphasize that an action was done without much consideration.Examples
把东西随便塞进提箱里
Just put things in the suitcase
bǎ dōngxi suíbiàn sāijìn tíxiāng lǐ
他在纸上胡乱画了几笔
He made a few strokes on the paper
tā zài zhǐ shàng húluàn huà le jǐbǐ
在城里他把所有的钱都胡乱花掉了
He wasted all his money in the city
zài chéng lǐ tā bǎ suǒyǒu de qián dōu húluàn huādiào le
这些话我不过随便说说罢了
I just said that for no reason
zhèxiē huà wǒ búguò suíbiàn shuōshuo bà le
Other meanings of 随便
随便 can also serve as an adjective and mean "random" and "casual".
Pay attention
胡乱 cannot serve as an adjective.
Examples
他对你在态度上过于随便
He treats you with indignity
tā duì nǐ zài tàidu shàng guòyú suíbiàn
跟他在一起很随便，一点儿也不拘束
I feel at ease and uninhibited with him
gēn tā zài yìqǐ hěn suíbiàn, yìdiǎnr yě bù jūshù
随便 can also be used in the meaning "anyhow, any".
Examples
晚饭你想吃小饺子还是披萨？—— 随便
Would you like dumplings or pizza for dinner? — Whatever
wǎnfàn nǐ xiǎng chī xiǎo jiǎozi háishi pīsà — suíbiàn