Final answer:
Monomials are single-term algebraic expressions comprising a constant, a variable, or the multiplication of a constant and variable(s). A number, a variable, and the product of a number and variables are all monomials, but sums and differences including variables are not.
Step-by-step explanation:
A monomial is an algebraic expression that has only one term. It can be a single number, a single variable, or the product of a number and one or more variables raised to whole number powers. There should not be any addition or subtraction within a monomial.
Based on these definitions:
A number (A) is a monomial because it is a constant, which qualifies as a single term.
A variable (B) is also a monomial, as it is a single term without any addition or subtraction involved.
The product of a number and one or more variables (E) is a monomial too, because it constitutes a single term where variables are possibly raised to whole number powers and multiplied by a coefficient.
However,
The sum of a number and one or more variables (C), and
The difference of a number and one or more variables (D)
are not monomials because they involve addition or subtraction, making them polynomials instead.