The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.2: Identifying Similar Terms

Understanding which terms are similar and which are not is an essential concept for adding and

subtracting polynomials. When students have difficulty adding and subtracting polynomials,

mistakes often arise from an inability to identify similar terms.

1. Explain that similar terms have the same variable to the same degree. Provide examples such
   as 3xand− 4 x,9yand 3y,− 5 x^2 and 8x^2 ,xyandyx,and5xy^3 andxy^3. Note that similar terms
   differ only in their numerical coefficient. The order in which the variables are written does
   not matter. If necessary, review monomial vocabulary, which is the focus of 5.1: ‘‘Applying
   Monomial Vocabulary Accurately.’’ Students need to understand terms such as ‘‘degree’’ and
   ‘‘coefficient’’ in order to complete Worksheet 5.2.


2. Provide examples of terms that are not similar, such asxandx^2 ,2xand 2y,and3x^2 and 3x^3 ,
   to further reinforce the concept of similar terms. Ask your students to explain why these
   pairs of terms are not similar.


3. Review the examples on the worksheet with your students.

EXTRA HELP:

Every term has a coefficient. If none is written, the coefficient is 1.

ANSWER KEY:

Pairs of similar terms follow: 3xand 7x;^1

5

x^2 and−x^2 ;6a^2 band

1

4

a^2 b;6aand−a; 8aband 2ba;

3 x^2 yand 6x^2 y

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(Challenge)They are similar. 3xis another way of expressing 3x^1.

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178 THE ALGEBRA TEACHER’S GUIDE