1. Adding and Subtracting Polynomials 7-6
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. Example 1: Adding and Subtracting Monomials
Add or Subtract..
A. 12p3 + 11p2 + 8p3
12p3 + 11p2 + 8p3
Identify like terms.
20p3 + 11p2
Combine like terms.
B. 5x2 – 6 – 3x + 8
Identify like terms.
5x2 – 6 – 3x + 8
5x2 – 3x + 2
Combine like terms.

4. Example 1: Adding and Subtracting Monomials
Add or Subtract..
C. t2 + 2s2 – 4t2 – s2
t2 + 2s2 – 4t2 – s2
Identify like terms.
–3t2 + s2
Combine like terms.
D. 10m2n + 4m2n – 8m2n
10m2n + 4m2n – 8m2n
Identify like terms.
6m2n
Combine like terms.

5. You try these!
Add or subtract.
a. 2s2 + 3s2 + s
Ans: 5s2 + s
b. 4z4 – z4 + 2
Ans: 20z4 – 6

6. Add or subtract.
c. 2x8 + 7y8 – x8 – y8
Ans: x8 + 6y8
d. 9b3c2 + 5b3c2 – 13b3c2
Ans: b3c2

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

8. Add.
A. (4m2 + 5) + (m2 – m + 6)
Ans: 5m2 – m + 11
B. (10xy + x) + (–3xy + y)
Ans: 7xy + x + y

9. Add.
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
Ans: x2 – 3y

10. Add.

11. You Try!
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
Ans:12a3 + 15a2 – 16a

12. Subtracting Polynomials
(x3 + 4y) – (2x3)
Ans: –x3 + 4y

13. Subtract.
(7m4 – 2m2) – (5m4 – 5m2 + 8)
Ans: 2m4 + 3m2 – 8

14. Subtract.
(–10x2 – 3x + 7) – (x2 – 9)
Ans: –11x2 – 3x + 16

15. Subtract.
(9q2 – 3q) – (q2 – 5)
Ans: 8q2 – 3q + 5

16. You Try!
Subtract.
(2x2 – 3x2 + 1) – (x2 + x + 1)
Ans: –2x2 – x

17. 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.
Plot A.
Plot B.
(3x2 + 7x – 5) +
(5x2 – 4x + 11)

18. 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)
5. (2.5ab + 14b) – (–1.5ab + 4b)

19. 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.