1. Objective
Add and subtract polynomials.

2. Example 1: Adding and Subtracting Monomials
Add or Subtract only monomials with the exact same letters AND exponents.
A. 12p3 + 11p2 + 8p3
12p3 + 11p2 + 8p3
Identify like terms.
Rearrange terms so that like terms are together.
12p3 + 8p3 + 11p2
20p3 + 11p2
Combine like terms.
B. 5x2 – 6 – 3x + 3x2 + 8
Identify like terms.
5x2 + 3x2 – 6 – 3x + 8
Rearrange terms so that like terms are together.
8x2 – 3x + 8 – 6
8x2 – 3x + 2
Combine like terms.

3. Example 1: Adding and Subtracting Monomials
Add or Subtract only monomials with the exact same letters AND exponents.
C. t2 + 2s2 – 4t2 – s2
t2 + 2s2 – 4t2 – s2
Identify like terms.
Rearrange terms so that like terms are together.
t2 – 4t2 + 2s2 – s2
–3t2 + s2
Combine like terms.
D. 10m2n + 4m2n – 8m2n
10m2n + 4m2n – 8m2n
Identify like terms.
6m2n
Combine like terms.

4. Check It Out! Example 1
Add or Subtract only monomials with the exact same letters AND exponents.
c. 2x6 + 7y8 – x6 + y2
Identify like terms.
2x6 + 7y8 – x6 – y2
Rearrange terms so that like terms are together.
2x6 – x6 + 7y8 – y2
x6 + 7y8 – y2
Combine like terms.
d. 9b3c2 + 5b3c2 – 10b2c2
9b3c2 + 5b3c2 – 10b2c2
Identify like terms.
14b3c2 – 10b2c2
Combine like terms.

5. Example 2: Adding Polynomials
Add or Subtract only monomials with the exact same letters AND exponents.
A. (4m2 + 5) + (m2 – m + 6)
(4m2 + 5) + (m2 – m + 6)
Identify like terms.
Group like terms together.
(4m2 + m2) + (–m) + (5 + 6)
5m2 – m + 11
Combine like terms.
B. (10xy + x + 3y) + (–3xy + y)
(10xy + x + 3y) + (–3xy + y)
Identify like terms.
Group like terms together.
10xy – 3xy + x + 3y + y
7xy + x + 4y
Combine like terms.

6. Check It Out! Example 2
Add or Subtract only monomials with the exact same letters AND exponents.
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
(5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a)
Identify like terms.
5a3 + 7a3 + 3a2 + 12a2 –10a – 6a
Group like terms together.
12a3 + 15a2 – 16a
Combine like terms.

7. Example 3B: Subtracting Polynomials
Subtract. DISTRIBUTE THE NEGATIVE
(7m4 – 2m2) – (5m4 – 5m2 + 8)
Distribute a -1 to everything in the second set of parentheses.
(7m4 – 2m2) + (–5m4 + 5m2 – 8)
7m4 – 2m2 –5m4 + 5m2 – 8
Identify like terms.
Group like terms together.
7m4 – 5m4 –2m2 + 5m2 – 8
2m4 + 3m2 – 8
Combine like terms.

8. Example 3D: Subtracting Polynomials
Subtract. DISTRIBUTE THE NEGATIVE
(9q2 – 3q) – (q2 – 5 - 3)
Distribute a -1 to everything in the second set of parentheses.
(9q2 – 3q) + (–q )
9q2 – 3q –q
Identify like terms.
Use the vertical method.
9q2 –q2 – 3q
Combine like terms.
8q2 – 3q + 8