Problem: Define x⊗y=x3−yx \otimes y=x^{3}-yx⊗y=x3−y. What is h⊗(h⊗h)?h \otimes(h \otimes h)?h⊗(h⊗h)?
Answer Choices:
A. −h-h−h B. 000 C. hhh D. 2h2 h2h E. h^
Solution:
By the definition we have
h⊗(h⊗h)=h⊗(h3−h)=h3−(h3−h)=(C)hh \otimes(h \otimes h)=h \otimes\left(h^{3}-h\right)=h^{3}-\left(h^{3}-h\right)= (\text{C})\boxed{h} h⊗(h⊗h)=h⊗(h3−h)=h3−(h3−h)=(C)h
The problems on this page are the property of the MAA's American Mathematics Competitions