which of the following expression does not contain any like terms?a.2x^2+3x-4x+2 b.xy+yz-17 c.x^3+x^2-2x-x^2 d.14+8+y
Looks like (B)
no two terms have the same variables to the same powers
To determine which expression does not contain any like terms, we need to identify like terms in each expression.
Like terms are terms that have the same variable(s) raised to the same exponent(s). For example, in the expression 2x^2 + 3x - 4x + 2, the terms 3x and -4x are like terms since they both have the variable x raised to the first power.
Let's analyze each expression:
a. 2x^2 + 3x - 4x + 2
The like terms here are 3x and -4x, both with the variable x raised to the first power. Therefore, this expression does contain like terms.
b. xy + yz - 17
There are no like terms in this expression because each term has different variables or different exponents on the same variables.
c. x^3 + x^2 - 2x - x^2
In this expression, the like terms are x^3 and -x^2, both with the variable x raised to a power. Therefore, this expression does contain like terms.
d. 14 + 8 + y
There are no like terms in this expression because there are no variables in the terms. They are all constants.
Therefore, the expression that does not contain any like terms is option b. xy + yz - 17.