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 (2)
A monomial is a single term expression.
Option A, 2 x − yz , has two terms and is not a monomial.
Option B, 2 + x yz , has two terms and is not a monomial.
Option C, 2 x y z 2 , has one term and is a monomial. Therefore, the answer is C .
Explanation
Understanding Monomials A monomial is an algebraic expression consisting of only one term. A monomial can be a number, a variable, or a product of numbers and variables with non-negative integer exponents. We need to identify which of the given expressions is a monomial.
Analyzing Option A Option A: 2 x − yz . This expression has two terms, 2 x and − yz , separated by subtraction. Therefore, it is not a monomial.
Analyzing Option B Option B: 2 + x yz . This expression has two terms, 2 and x yz , separated by addition. Therefore, it is not a monomial.
Analyzing Option C Option C: 2 x y z 2 . This expression has only one term, which is a product of a constant and variables. Therefore, it is a monomial.
Analyzing Option D Option D: 2 x + yz . This expression has two terms, 2 x and yz , separated by addition. Therefore, it is not a monomial.
Conclusion The expression that is a monomial is 2 x y z 2 . Therefore, the correct answer is C.
Examples
Monomials are fundamental in algebra, serving as building blocks for more complex expressions. For instance, calculating the area of a rectangle with sides 2 x and 3 y involves multiplying these monomials to get the area 6 x y . Similarly, in physics, the kinetic energy of an object can be expressed as 2 1 m v 2 , where m (mass) and v (velocity) can be seen as monomials. Understanding monomials helps simplify and solve real-world problems in various fields.
The only option that is a monomial is Option C: 2 x y z 2 , as it consists of only one term. The other options include additional terms through addition or subtraction, which disqualifies them as monomials.
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