Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.

1. Adding and Subtracting
Polynomials

2. Adding Polynomials
When adding polynomials, you are simply
combining like terms.
Remember that “like terms” must have the
same base and the same exponent. You add
the coefficients.

3. Add or subtract.
Additional Example 1: Adding and Subtracting
Monomials
A. 12p3
+ 11p2
+ 8p3
12p3
+ 11p2
+ 8p3
12p3
+ 8p3
+ 11p2
20p3
+ 11p2
Identify like terms.
Rearrange terms so that like
terms are together.
Combine like terms.
B. 5x2
– 6 – 3x + 8
5x2
– 6 – 3x + 8
5x2
– 3x + 8 – 6
5x2
– 3x + 2
Identify like terms.
Rearrange terms so that like
terms are together.
Combine like terms.

4. Add or subtract.
Additional Example 1: Adding and Subtracting
Monomials
C. t2
+ 2s2
– 4t2
– s2
t2
– 4t2
+ 2s2
– s2
t2
+ 2s2
– 4t2
– s2
–3t2
+ s2
Identify like terms.
Rearrange terms so that
like terms are together.
Combine like terms.
D. 10m2
n + 4m2
n – 8m2
n
10m2
n + 4m2
n – 8m2
n
6m2
n
Identify like terms.
Combine like terms.

5. Add.
Additional Example 2: Adding Polynomials
A. (4m2
+ 5) + (m2
– m + 6)
(4m2
+ 5) + (m2
– m + 6)
(4m2
+ m2
) + (–m) + (5 + 6)
5m2
– m + 11
Identify like terms.
Group like terms
together.
Combine like terms.
B. (10xy + x) + (–3xy + y)
(10xy + x) + (–3xy + y)
(10xy – 3xy) + x + y
7xy + x + y
Identify like terms.
Group like terms
together.
Combine like terms.

6. To subtract polynomials, remember that
subtracting is the same as adding the
opposite. To find the opposite of a
polynomial, you must write the opposite of
each term in the polynomial:
–(2x3
– 3x + 7) = –2x3
+ 3x – 7

7. Subtract.
Additional Example 3A: Subtracting Polynomials
(x3
+ 4y) – (2x3
)
(x3
+ 4y) + (–2x3
)
(x3
+ 4y) + (–2x3
)
(x3
– 2x3
) + 4y
–x3
+ 4y
Rewrite subtraction as addition
of the opposite.
Identify like terms.
Group like terms together.
Combine like terms.

8. Subtract.
Additional Example 3B: Subtracting Polynomials
(7m4
– 2m2
) – (5m4
– 5m2
+ 8)
(7m4
– 2m2
) + (–5m4
+ 5m2
– 8)
(7m4
– 5m4
) + (–2m2
+ 5m2
) – 8
(7m4
– 2m2
) + (–5m4
+ 5m2
– 8)
2m4
+ 3m2
– 8
Rewrite subtraction as
addition of the opposite.
Identify like terms.
Group like terms
together.
Combine like terms.