Final answer:
The given algebraic expression simplifies to Y - 8y^3, as x^0 equals 1 and subtracting zero does not change the value of an expression.
Step-by-step explanation:
The question pertains to identifying expressions equivalent to a given algebraic expression. In algebra, expressions can often be rewritten in different forms that are still equivalent, meaning they have the same value for all values of the variables involved. One important concept to recall is that any variable raised to the power of 0 is equal to 1 (x^0 = 1), and multiplying by zero results in zero. Thus, in the given expression Y - 8y^3x^0x - 0, the term x^0 is equal to 1, simplifying the expression to Y - 8y^3 - 0 which simplifies further to Y - 8y^3, as subtracting zero does not change the value.
As such, the other expressions must also result in Y - 8y^3 when they are simplified to be considered equivalent to the original expression.