Select the best answer for the question.
Which of the following is a monomial?
A. [tex]$2 x+y z$[/tex]
B. [tex]$2+x y z$[/tex]
C. [tex]$2 x y z^2$[/tex]
D. [tex]$2 x-y z$[/tex]
Answer (1)
A monomial is an expression with only one term. Among the options, only 2 x y z 2 fits this definition.
Option A, 2 x + yz , has two terms.
Option B, 2 + x yz , has two terms.
Option C, 2 x y z 2 , has one term and is a monomial.
Option D, 2 x − yz , has two terms. Therefore, the answer is C .
Explanation
Understanding Monomials A monomial is an algebraic expression consisting of only one term. It can be a number, a variable, or a product of numbers and variables with non-negative integer exponents. Let's examine each option:
Analyzing Option A Option A: 2 x + yz has two terms separated by an addition sign. Therefore, it is not a monomial.
Analyzing Option B Option B: 2 + x yz has two terms separated by an addition sign. Therefore, it is not a monomial.
Analyzing Option C Option C: 2 x y z 2 has only one term, which is a product of a constant and variables with non-negative integer exponents. Therefore, it is a monomial.
Analyzing Option D Option D: 2 x − yz has two terms separated by a subtraction sign. Therefore, it is not a monomial.
Conclusion Based on the analysis, the only monomial among the given options is 2 x y z 2 .
Examples
Monomials are fundamental in algebra, serving as building blocks for more complex expressions. For instance, when calculating the area of a rectangle with sides 2 x and 3 y , the area is represented by the monomial 6 x y . Similarly, in physics, the kinetic energy of an object can be expressed as 2 1 m v 2 , which is also a monomial. Understanding monomials is crucial for simplifying expressions, solving equations, and modeling real-world phenomena.
