Which of the following are like terms? Check all that apply.
4x and 4y
4x and 1/4x
-15y and 25y
9xy and 9
-11xy and -11x
4x and 1/4x
Like terms are terms that have the same variables raised to the same powers. Let's check each pair of terms:
4x and 4y: These terms do not have the same variables or exponent, so they are not like terms.
4x and 1/4x: These terms have the same variable (x), but they do not have the same exponent or coefficient, so they are not like terms.
-15y and 25y: These terms have the same variable (y), but they do not have the same exponent or coefficient, so they are not like terms.
9xy and 9: These terms have the same variable (xy), but the second term does not have an exponent, so they are not like terms.
-11xy and -11x: These terms have the same variable (x), but they do not have the same exponent or coefficient, so they are not like terms.
Therefore, the like terms are none of the above.
Like terms are terms that have the same variable(s) raised to the same power(s). In order to determine which of the given pairs are like terms, we need to compare the variables and their exponents.
Let's analyze each pair:
1. 4x and 4y: Since x and y are different variables, they are not like terms.
2. 4x and 1/4x: The variables are the same (x), but the exponents are different. One has a coefficient of 4, while the other has a coefficient of 1/4. Therefore, they are not like terms.
3. -15y and 25y: Both terms have the same variable (y) raised to the same power (1) and coefficients of -15 and 25 respectively. Thus, they are like terms.
4. 9xy and 9: The terms have different variables (xy and 1), thus they are not like terms.
5. -11xy and -11x: Both terms have the same variable (x) raised to the same power (1) and coefficients of -11. They are like terms.
Therefore, the like terms in the given list are:
-15y and 25y
-11xy and -11x