1. Page 680 #20-24 Pre-Algebra HOMEWORK Adding Polynomials 13-3

2. Pre-Algebra
13-1
Polynomials
Our Learning Goal
Students will be able to classify, simplify, add and subtract polynomials.

3. Pre-Algebra
13-1
Polynomials
Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments.
Learn to classify polynomials by degree and by the number of terms.
Learn to simplify polynomials.
Learn to add polynomials.
Learn to subtract polynomials.
…..and that’s all folks!

4. Today’s Learning Goal Assignment
Pre-Algebra
13-3
Adding Polynomials
Today’s Learning Goal Assignment
Learn to add polynomials.

5. Adding Polynomials 13-3 Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

6. Adding Polynomials 13-3 Warm Up Combine like terms.
Pre-Algebra
13-3
Adding Polynomials
Warm Up
Combine like terms.
1. 9x + 4x 2. –3y + 7y
3. 7n + (–8n) + 12n
Find the perimeter of each rectangle.
4. a 10 ft by 12 ft rectangle
5. a 5 m by 8 m rectangle
Simplify.
6. 3(2x2 – x) + x2+ 1
13x 4y
11n
44 ft
26 m
7x2 – 3x + 1

7. Adding Polynomials 13-3 Problem of the Day
Pre-Algebra
13-3
Adding Polynomials
Problem of the Day
Michael has a collection of dimes and quarters worth $6.55. If he has one more quarter than he has dimes, how many of each coin does he have?
18 dimes and 19 quarters

8. Pre-Algebra
13-3
Adding Polynomials
Learn to add polynomials.

9. Additional Example 1A: Adding Polynomials Horizontally
Pre-Algebra
13-3
Adding Polynomials
Additional Example 1A: Adding Polynomials Horizontally
Add.
A. (5x3 + x2 + 2) + (4x3 + 6x2)
(5x + x + 2) + (4x + 6x ) 3 2
5x + x x + 6x 3 2
Associative Property
9x + 7x + 2 3 2
Combine like terms.

10. Adding Polynomials 13-3 Try This: Example 1A Add.
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 1A
Add.
A. (3y4 + y2 + 6) + (5y4 + 2y2)
(3y + y + 6) + (5y + 2y ) 4 2
3y + y y + 2y 4 2
Associative Property
8y + 3y + 6 4 2
Combine like terms.

11. Additional Example 1B: Adding Polynomials Horizontally
Pre-Algebra
13-3
Adding Polynomials
Additional Example 1B: Adding Polynomials Horizontally
Add.
B. (6x3+ 8y2 + 5xy) + (4xy – 2y2)
(6x3+ 8y2+ 5xy) + (4xy – 2y2)
6x3 + 8y2 + 5xy + 4xy – 2y2
Associative Property
6x + 6y + 9xy 3 2
Combine like terms.

12. Adding Polynomials 13-3 Try This: Example 1B Add.
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 1B
Add.
B. (9x3 + 6p2 + 3xy) + (8xy – 3p2)
(9x + 6p + 3xy) + (8xy – 3p ) 3 2
9x + 6p + 3xy + 8xy – 3p 3 2
Associative Property
9x3+ 3p2+ 11xy
Combine like terms.

13. Additional Example 1C: Adding Polynomials Horizontally
Pre-Algebra
13-3
Adding Polynomials
Additional Example 1C: Adding Polynomials Horizontally
Add.
C. (3x2y – 5x) + (4x + 7) + 6x2y
(3x2y – 5x) + (4x + 7) + 6x2y
3x2y – 5x + 4x x2y
Associative Property
9x2y – x + 7
Combine like terms.

14. Adding Polynomials 13-3 Try This: Example 1C Add.
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 1C
Add.
C. (3z2w – 5x) + (2x + 8) + 6z2w
(3z2w – 5x) + (2x + 8) + 6z2w
3z2w – 5x + 2x z2w
Associative Property
9z2w – 3x + 8
Combine like terms.

15. Pre-Algebra
13-3
Adding Polynomials
You can also add polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms. If the terms are rearranged, remember to keep the correct sign with each term.

16. Additional Example 2A: Adding Polynomials Vertically
Pre-Algebra
13-3
Adding Polynomials
Additional Example 2A: Adding Polynomials Vertically
Add.
A. (4x2 + 2x + 11) + (2x2 + 6x + 9)
4x2 + 2x + 11
+ 2x2 + 6x + 9
Place like terms in columns.
6x2 + 8x + 20
Combine like terms.

17. Adding Polynomials 13-3 Try This: Example 2A Add.
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 2A
Add.
A. (6x2 + 6x + 13) + (3x2+ 2x + 4)
6x2 + 6x + 13
+ 3x2 + 2x + 4
Place like terms in columns.
9x2 + 8x + 17
Combine like terms.

18. Additional Example 2B & 2C: Adding Polynomials Vertically
Pre-Algebra
13-3
Adding Polynomials
Additional Example 2B & 2C: Adding Polynomials Vertically
Add.
B. (3mn2 – 6m + 6n) + (5mn2 + 2m – 6n)
C. (–x2y2 + 5x2) + (–2y2 + 2) + (x2 + 8)
3mn2 – 6m + 6n
+ 5mn2 + 2m – n
Place like terms in columns.
8mn2 – 4m + 5n
Combine like terms.
–x2y2 + 5x2
–2y2 + 2
Place like terms in columns. x
–x2y2 + 6x2 – 2y2 +10
Combine like terms.

19. Adding Polynomials 13-3 Try This: Example 2B & 2C Add.
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 2B & 2C
Add.
B. (4mn2 + 6m + 2n) + (2mn2 – 2m – 2n)
C. (x2y2 – 5x2) + (2y2 – 2) + (x2)
4mn2 + 6m + 2n
+ 2mn2 – 2m – 2n
Place like terms in columns.
6mn2 + 4m
Combine like terms.
x2y2 – 5x2
2y2 – 2
Place like terms in columns. x2
x2y2 – 4x2 + 2y2 – 2
Combine like terms.

20. Additional Example 3: Application
Pre-Algebra
13-3
Adding Polynomials
Additional Example 3: Application
Rachel wants to frame two photographs. The first photograph has dimensions b inches and h inches, and each dimension of the other photograph is twice the corresponding dimension of the first. She needs enough wood for the frames to cover both perimeters, and the width of the wood is 1 inches. Find an expression for the length of wood she needs to frame both photographs.
1 2

21. Additional Example 3 Continued
Pre-Algebra
13-3
Adding Polynomials
Additional Example 3 Continued
Perimeter of photograph 1:
Perimeter of photograph 2:
P = 2b + 2h + 12
P = 4b + 4h + 12
P = (2b + 2h + 12) + (4b + 4h + 12)
= 2b + 2h b + 4h + 12
= 6b + 6h + 24
Combine like terms.
She will need 6b + 6h + 24 in. of wood.

22. Adding Polynomials 13-3 Try This: Example 3
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 3
Michael wants to frame two photographs. The first photograph had dimensions b inches and h inches, and each dimension of the other photograph is three times the corresponding dimension of the first. He needs enough wood for the frames to cover both perimeters and the width of the wood is 2 inches. Find an expression for the length of wood he will need to frame both photographs.

23. Try This: Example 3 Continued
Pre-Algebra
13-3
Adding Polynomials
Try This: Example 3 Continued
Perimeter of photograph 1:
Perimeter of photograph 2:
P = 2b + 2h + 16
P = 6b + 6h + 16
P = (2b + 2h + 16) + (6b + 6h + 16)
= 2b + 2h b + 6h + 16
= 8b + 8h + 32
Combine like terms.
He will need 8b + 8h + 32 in. of wood.

24. Insert Lesson Title Here
Pre-Algebra
13-3
Adding Polynomials
Insert Lesson Title Here
Lesson Quiz: Part 1
Add.
1. (2m2 – 3m + 7) + (7m2 – 1)
2. (yz2 + 5yz + 7) + (2yz2 – yz) 3.
9m2 – 3m + 6
3yz2+ 4yz + 7
(2xy2 + 2x – 6)
+ (5xy2 + 3y + 8)
7xy + 2x + 3y + 2 2

25. Insert Lesson Title Here
Pre-Algebra
13-3
Adding Polynomials
Insert Lesson Title Here
Lesson Quiz: Part 2
(3np3 + 4n)
(5np3 – n – 6) (2n – 3)
5. The base of an isosceles triangle has length x + 4. The two legs of the triangle have lengths 3x + y. Write an expression for the perimeter of the triangle.
8np3 + 5n – 9
7x + 2y+ 4