Question

Ms. Fisher's students are working on identifying like terms in algebraic expressions. When Ms. Fisher asks them how they know when terms are like terms, one student, Coleman, says, "Like terms have to have the same variable in them." Ms. Fisher wants to use a pair of terms to show Coleman that his description of like terms is incomplete and needs to be refined. Which of the following pairs of terms is best for Ms. Fisher to use for this purpose?

A. 3x and 4y
B. 2x and 5x
C. 2y and 7z
D. 4x and 6y

Answer 1

The best pair of terms to show Coleman that like terms need to have the same variable as well as the same exponents is 3x and 4y, as they have different variables.

Step-by-step explanation:

Coleman's description of like terms as terms that have the same variable is a good start, but it needs to be more specific. Like terms must have not only the same variable, but also the same exponents on that variable. Therefore, the best pair of terms to show that same variables alone do not make terms 'like' would be Option A: 3x and 4y. These terms both have variables, but they are not the same variable, hence they cannot be combined as like terms.