Define x⨂y = x^3 - y. Simplify h ⨂ (h⨂h).
To simplify the expression h ⨂ (h ⨂ h), we need to substitute the value of h into the definition of the operation ⨂.
Given that x⨂y = x^3 - y, we substitute h for x and (h ⨂ h) for y:
h⨂(h⨂h) = h^3 - (h⨂h)
We can simplify this expression further by substituting the value of h for (h⨂h):
h^3 - (h⨂h) = h^3 - (h^3 - h)
Expanding further, we simplify the expression:
h^3 - (h^3 - h) = h^3 - h^3 + h = h