1. Adding and Subtracting Polynomials
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1

2. Warm Up Simplify each expression by combining like terms. 1. 4x + 2x
2. 3y + 7y
3. 8p – 5p
4. 5n + 6n2
Simplify each expression.
5. 3(x + 4)
6. –2(t + 3)
7. –1(x2 – 4x – 6) 6x
10y 3p
not like terms
3x + 12
–2t – 6
–x2 + 4x + 6

3. Objective
Add and subtract polynomials.

4. Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

5. Example 1: Adding and Subtracting Monomials
Add or Subtract..
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

6. Example 1: Adding and Subtracting Monomials
Add or Subtract..
C. t2 + 2s2 – 4t2 – s2
D. 10m2n + 4m2n – 8m2n

7. Add or subtract.
E. 2s2 + 3s2 + s
F. 4z4 – z4 + 2

8. Add or subtract.
G. 2x8 + 7y8 – x8 – y8
H. 9b3c2 + 5b3c2 – 13b3c2

9. Polynomials can be added in either vertical or horizontal form.
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 + 1) + (4x + 5x) + (1 + 2)
= 7x2 + 9x + 3

10. 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)

11. Example 2C: Adding Polynomials
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)

12. Example 2D: Adding Polynomials

13. Check It Out! Example 2
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).

14. 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

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

16. Example 3B: Subtracting Polynomials
(7m4 – 2m2) – (5m4 – 5m2 + 8)

17. Example 3C: Subtracting Polynomials
(–10x2 – 3x + 7) – (x2 – 9)

18. Example 3D: Subtracting Polynomials
(9q2 – 3q) – (q2 – 5)

19. Check It Out! Example 3
Subtract.
(2x2 – 3x2 + 1) – (x2 + x + 1)

20. Example 4: Application
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x Write a polynomial that represents the total area of both plots of land.

21. Lesson Quiz: Part I
Add or subtract.
1. 7m2 + 3m + 4m2
2. (r2 + s2) – (5r2 + 4s2)
3. (10pq + 3p) + (2pq – 5p + 6pq)
4. (14d2 – 8) + (6d2 – 2d +1)
11m2 + 3m
(–4r2 – 3s2)
18pq – 2p
20d2 – 2d – 7
5. (2.5ab + 14b) – (–1.5ab + 4b)
4ab + 10b

22. Lesson Quiz: Part II
6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x2 + 12x + 9, and the area of the second wall is modeled by
36x2 – 12x + 1. Write a polynomial that represents the total area of the two walls.
40x2 + 10