Common Algebra Mistakes
Example: Radical Expressions  Distance Formula 
The Goal
Find the distance D between the points (x,0,0) and (x,y,z) in 3space. The Mistake
Find the algebra mistake: (Roll the mouse over the algebra to see a hint in red) The Correction
(Roll the mouse over the area above to see the correction in blue) An Explanation The mistake is in the final step  it is incorrect to distribute the square root over the sum. That is: Try it with some numbers to convince yourself: let A=1 and B=1. The left side is √2, while the right side is 2. One counterexample disproves a general formula. 
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