Adding and Subtracting Polynomials 87
Like Terms
Monomials that are constants or that have exactly the same variable factors
(i.e., the same letters with the same corresponding exponents) are like terms.
Like terms are the same except, perhaps, for their coeffi cients.
Problem State whether the given monomials are like terms. Explain your
answer.
a. 10 x and 2 5 x
b. 4 xy^232 and − 7 xy^323
c. 100 and 45
d. 25 and 2 5 x
Solution
a. − 10 x and 25 x
Step 1. Check whether − 10 x and 2 5 x meet the criteria for like terms.
− 10 x and^25 x are like terms because they are exactly the same
except for their numerical coeffi cients.
b. 4 xy^232 and − 7 xy^323
Step 1. Check whether 4 x^23 y and − 7 x^32 y meet the criteria for like terms.
4 xy^23 and − 7 xy^32 are not like terms because the corresponding
exponents on x and y are not the same.
c. 100 and 45
Step 1. Check whether 100 and 45 meet the criteria for like terms.
100 and 45 are like terms because they are both constants.
d. 25 and 25 x
Step 1. Check whether 25 and 2 5 x meet the criteria for like terms.
25 and 25 x are not like terms because they do not contain the same
variable factors.
Finally, monomials that are not like terms are unlike terms.
