I am pretty sure you can make them as hard as you want - if you have a "hard" problem, you can always find one that is even harder. If this is true, then there is no such thing as a "hardest algebra problem".
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It is difficult to say. First, different people find different things hard or easy. So something that you find hard I might find easy and conversely. Second, there are still unsolved questions in algebra and until they are solved no one can say which one of them is harder. And finally, it is possible that the really hardest problem is yet to be discovered.
high school algebra CORRECT ANSWER: Linear Algebra in high school.
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The easiest way to solve an algebra problem is to work out the problem.
Not easy...