2006 AMC 12A Problems/Problem 2

Problem

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

$\mathrm{(A)}\ -h\qquad\mathrm{(B)}\ 0\qquad\mathrm{(C)}\ h\qquad\mathrm{(D)}\ 2h \mathrm{(E)}\ h^3$

Solution

By the definition of $\otimes$ , we have $h\otimes h=h^{3}-h$ . Then $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=h$ . The answer is $\mathrm{(C)}$ .

2006 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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2006 AMC 12A Problems/Problem 2

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