The question is asking us to determine which of the given expressions does not belong to the group based on their structure and form. Let us analyze each expression one-by-one.
A. ¼x⁴-1
This is a monomial expression. A monomial is an algebraic expression consisting of a single term. It doesn't involve any additional variables.
B. X²-0.0001y⁴
This is a polynomial expression with more than one variable (x and y). A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variables.
C. 8(X-1)³-27
This is an expression that includes powers (cubed exponent) and a subtraction operation. It's important to note that it only contains a single variable (x).
D. (X+1)⁴ -4x⁴
Similar to C, this is also an expression that includes powers (to the fourth exponent) and a subtraction operation, and also only contains one variable (x).
Upon comparing all four expressions, we can see that choice B is the one that doesn't belong to the group. It is the only polynomial expression that contains more than one variable (multi-variable). The other expressions A, C and D all contain single variables (mono-variable expressions). Therefore, the answer is B.
Answer: B. X²-0.0001y⁴