To classify the expressions x²y, 7xy, xyz, and x by their degree and terms, we need to analyze each term individually.
- x²y: This term has two variables (x and y). The degree of this term is calculated by adding the exponents of its variables: 2 (from x²) + 1 (from y) = 3. So, this term is a monomial of degree 3.
- 7xy: In this case, the term consists of the coefficient 7 and the variables x and y. The degree is determined by summing the exponents: 1 (from x) + 1 (from y) = 2. Therefore, 7xy is a monomial of degree 2.
- xyz: This term includes three variables: x, y, and z. The degree is calculated as 1 (from x) + 1 (from y) + 1 (from z) = 3. Consequently, xyz is a monomial of degree 3.
- x: This term has only one variable, x. The degree is 1 (since x is equivalent to x¹), making it a monomial of degree 1.
In summary, all four expressions are monomials, with degrees classified as follows:
- x²y: degree 3
- 7xy: degree 2
- xyz: degree 3
- x: degree 1