1. Adding and Subtracting Polynomials 6-4
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Holt Algebra 1

2. Warm Up 01/06/17 Simplify each expression by combining like terms.
1. 4x + 2x
2. 8p – 5p
Simplify each expression.
3. 3(x + 4)
4. –1(x2 – 4x – 6)

3. Essential 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: Adding and Subtracting Monomials
A. 12p3 + 11p2 + 8p3
Identify like terms.
12p3 + 11p2 + 8p3
20p3 + 11p2
Combine like terms.
B. 5x2 – 6 – 3x + 8
5x2 – 6 – 3x + 8
Identify like terms.
5x2 – 3x + 2
Combine like terms.

6. I do….
C. t2 + 2s2 – 4t2 – s2
t2 + 2s2 – 4t2 – s2
Identify like terms.
t2 – 4t2 + 2s2 – s2
–3t2 + s2
D. 10m2n + 4m2n – 8m2n
10m2n + 4m2n – 8m2n
Identify like terms.
6m2n

7. Like terms are constants or terms with the same variable(s) raised to the same power(s).
Remember!

8. We d0....
Add or subtract.
a. 2s2 + 3s2 + s
2s2 + 3s2 + s
5s2 + s
b. 4z4 – z4 + 2
4z4 – z4 + 2
4z4 + 16z4 – 8 + 2
20z4 – 6

9. You do….
Add or subtract.
c. 2x8 + 7y8 – x8 – y8
x8 + 6y8
d. 9b3c2 + 5b3c2 – 13b3c2
b3c2

10. 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) + (4x + 5x) + (1 + 2)
= 7x2 + 9x + 3

11. Example: Adding Polynomials

12. 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 signs of each term:
Change the signs and proceed to addition!
–(2x3 – 3x + 7)= –2x3 + 3x – 7

13. Example: Subtracting Polynomials
(x3 + 4y) – (2x3)
Rewrite subtraction as addition of the opposite.
(x3 + 4y) + (–2x3)
(x3 + 4y) + (–2x3)
(x3 – 2x3) + 4y
–x3 + 4y
Combine like terms.

14. We do….
Subtract.
(–10x2 – 3x + 7) – (x2 – 9)
(–10x2 – 3x + 7) + (–x2 + 9)
(–10x2 – 3x + 7) + (–x2 + 9)
–10x2 – 3x + 7
–x2 + 0x + 9
–11x2 – 3x + 16

15. You do….
Subtract.
(9q2 – 3q) – (q2 – 5)
(9q2 – 3q) + (–q2 + 5)
(9q2 – 3q) + (–q2 + 5)
9q2 – 3q + 0
+ − q2 – 0q + 5
8q2 – 3q + 5

16. Example: 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.
(3x2 + 7x – 5)
Plot A. +
(5x2 – 4x + 11)
Plot B.
8x2 + 3x + 6
Combine like terms.

17. Lesson Quiz /06/17
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)