1. went to Poly- Nomial’s house to visit her Ma-Nomial who had a son,
Adding Polynomials
Mr. Peter Richard
went to Poly- Nomial’s house to visit her Ma-Nomial who had a son,
Bi-Nomial. Bi-Nomial had a son called Tri-Nomial, but don’t ask me how this happened. Mr. Peter Richard obtained very valuable information about how the Nomials function. He passes this secret knowledge unto you free of charge.

2. Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.
Like terms are constants or terms with the same variable(s) raised to the same power(s).
Remember!

3. Example 1: Adding and Subtracting Monomials
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 + 8
Identify like terms.
5x2 – 6 – 3x + 8
Rearrange terms so that like terms are together.
5x2 – 3x + 8 – 6
5x2 – 3x + 2
Combine like terms.

4. Example 1: Adding and Subtracting Monomials
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.

5. Check It Out! Example 1
Add
a. 2s2 + 3s2 + s
2s2 + 3s2 + s
Identify like terms.
5s2 + s
Combine like terms.
b. 4z4 – z4 + 2
4z4 – z4 + 2
Identify like terms.
Rearrange terms so that like terms are together.
4z4 + 16z4 – 8 + 2
20z4 – 6
Combine like terms.

6. Check It Out! Example 1
Add
c. 2x8 + 7y8 – x8 – y8
Identify like terms.
2x8 + 7y8 – x8 – y8
Rearrange terms so that like terms are together.
2x8 – x8 + 7y8 – y8
x8 + 6y8
Combine like terms.
d. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
Identify like terms.
b3c2
Combine like terms.

7. Polynomials can be added in either vertical or horizontal form.
(5x2 + 4x + 1) + (2x2 + 5x + 2)
In vertical form, align the like terms and add:
In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.
5x2 + 4x + 1
+ 2x2 + 5x + 2
7x2 + 9x + 3
(5x2 + 4x + 1) + (2x2 + 5x + 2)
= (5x2 + 2x2) + (4x + 5x) + (1 + 2)
= 7x2 + 9x + 3

8. Example 2: Adding Polynomials
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) + (–3xy + y)
(10xy + x) + (–3xy + y)
Identify like terms.
Group like terms together.
(10xy – 3xy) + x + y
7xy + x + y
Combine like terms.

9. Example 2C: Adding Polynomials
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
Identify like terms.
Group like terms together within each polynomial.
(6x2 + 3x2 – 8x2) + (3y – 4y – 2y)
6x2 – 4y
+ –5x2 + y
Use the vertical method.
Combine like terms.
x2 – 3y
Simplify.

10. Example 2D: Adding Polynomials
Identify like terms.
Group like terms together.
Combine like terms.

11. Check It Out! Example 2
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.

12. Time to Polynomialize! Quiz: Page 497/498 # 22, 24, 26, 38, 46
Homework: # 21, 23, 27, 35, 47