Distributive Genie
A teacher's final wish to a genie is that people stop thinking (a + b)² = a² + b²; even the genie's area-model lesson fails when a student asks about square roots.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2018-01-08-distributive-genie/ (CC BY-NC 4.0)Transcript
Genie: "And for your final wish...?" A: "I wish people understood that (a + b)² isn't a² + b²." Genie: "It is done."
[Genie at a board with an area model: a², b², and the leftover rectangles] Student: "But... √(a + b) is still √a + √b, right?"
Genie: "I'm sorry... I tried, but..." A: "No worries. It's actually kind of validating for me that you couldn't manage, either."