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2006 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

Define x⊗y=x3−y.x \otimes y = x^3 - y. What is h⊗(h⊗h)?h \otimes (h \otimes h)?

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Solution

By the definition, h⊗h=h3−h.h \otimes h = h^3 - h. Then h⊗(h3−h)=h3−(h3−h)=h. \begin{gathered} h \otimes (h^3 - h) \\ = h^3 - (h^3 - h) \\ = h. \end{gathered} Thus, the correct answer is C.

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Concepts: custom operation · substitution

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