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Because sometimes people make mistakes in their head, and showing the step-by-step process is like proofreading an essay. Sure, anyone can whip out a quality essay, but being careful and checking for errors along the way never hurt anyone.

My Algebra 2/Pre Cal teacher had the best policy to create a compromise. She said we didn't have to show our work, but she would give us "pity points" for each step-by-step process that was correct. You can do it in your head and on your own, but it's a zero if it's incorrect.