One of the biggest problems is that there are so many different concepts and equations in algebra and in order to be successful you have to understand the entirety of it or you will not be able to figure out which procedure to use. You learned the order of operations years ago and that is one key tool for algebra. This tool allows you to understand which process happens first and so on. PEMDAS is a very valuable tool.
What it is about memorizing multiplication tables that make my kids throw their pencil across the room and shout, “I hate math?” It is because, unlike spelling or vocabulary, numbers don’t create pictures for us. Multiplication tables are strings of seemingly random numbers that our children are expected to not only remember, but keep in order and in context with the numbers they are multiplying by.