Adding and Subtracting Polynomials 89
4 xy^23 and 7 xy^32 are not like terms, so leave the problem as indicated
subtraction: 47 xy^23 xy^32.
c. 9 xx^2233333 x^2 − 7 x^2
Step 1. Check for like terms.
9 xxx^2233333 x^2772
97 x^22 ,,x and x^2 are like terms.
Step 2. Combine the numerical coeffi cients.
933 − 75
Step 3. Use the result as the coeffi cient of x^2.
9 xxx^2233333 x^2757225 x
d. 25 + 25 x
Step 1. Check for like terms.
25 +^25 x
25 and 25x are not like terms, so leave the
problem as indicated addition: 25 + 25x.
e. 5 xx^22777
Step 1. Check for like terms.
57
xx^2277
57
xx^2277 are like terms.
Step 2. Subtract the numerical coeffi cients.
577 =−^2
Step 3. Use the result as the coeffi cient of x^2.
57 xx^22777 x =− 2 x^2
Combining Like Terms
When you have an assortment of like terms in the same expression, system-
atically combine matching like terms in the expression. (For example, you
might proceed from left to right.) To organize the process, use the properties
25 +≠ 2525 ≠ 5050 x. These are not
like terms, so you cannot combine
them into one single term.
