1. Combine like terms. 1. 9x + 4x2. –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(2x 2 – x) + x 2 + 1 13x 4y4y 11n 44 ft 26 m 7x 2 – 3x + 1 Warm Up

2. Pre-Algebra Adding Polynomials 13-3

3. Learn to add polynomials.

4. Add. A. (5x 3 + x 2 + 2) + (4x 3 + 6x 2 ) (5x + x + 2) + (4x + 6x ) 3 2 3 2 5x + x + 2 + 4x + 6x 3 2 3 2 9x + 7x + 2 3 2 Associative PropertyCombine like terms. Example: Adding Polynomials Horizontally

5. Add. B. (6x 3 + 8y 2 + 5xy) + (4xy – 2y 2 ) (6x 3 + 8y 2 + 5xy) + (4xy – 2y 2 ) 6x 3 + 8y 2 + 5xy + 4xy – 2y 2 6x + 6y + 9xy 3 2 Associative PropertyCombine like terms. Example: Adding Polynomials Horizontally

6. Add. C. (3x 2 y – 5x) + (4x + 7) + 6x 2 y (3x 2 y – 5x) + (4x + 7) + 6x 2 y 9x 2 y – x + 7 Associative PropertyCombine like terms. 3x 2 y – 5x + 4x + 7 + 6x 2 y Example: Adding Polynomials Horizontally

7. Add. A. (3y 4 + y 2 + 6) + (5y 4 + 2y 2 ) (3y + y + 6) + (5y + 2y ) 4 2 4 2 3y + y + 6 + 5y + 2y 4 2 4 2 8y + 3y + 6 4 2 Associative PropertyCombine like terms. Try This

8. Add. B. (9x 3 + 6p 2 + 3xy) + (8xy – 3p 2 ) (9x + 6p + 3xy) + (8xy – 3p ) 3 2 2 9x + 6p + 3xy + 8xy – 3p 3 2 2 9x 3 + 3p 2 + 11xy Associative PropertyCombine like terms. Try This

9. Add. C. (3z 2 w – 5x) + (2x + 8) + 6z 2 w (3z 2 w – 5x) + (2x + 8) + 6z 2 w 9z 2 w – 3x + 8 Associative PropertyCombine like terms. 3z 2 w – 5x + 2x + 8 + 6z 2 w Try This

10. 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.

11. Add. A. (4x 2 + 2x + 11) + (2x 2 + 6x + 9) 4x 2 + 2x + 11 + 2x 2 + 6x + 9 6x 2 + 8x + 20 Combine like terms. Place like terms in columns. Example: Adding Polynomials Vertically

12. Add. B. (3mn 2 – 6m + 6n) + (5mn 2 + 2m – 6n) C. (–x 2 y 2 + 5x 2 ) + (–2y 2 + 2) + (x 2 + 8) + 5mn 2 + 2m – n 8mn 2 – 4m + 5n –2y 2 + 2 + x 2 + 8 –x 2 y 2 + 6x 2 – 2y 2 +10 3mn 2 – 6m + 6n –x 2 y 2 + 5x 2 Combine like terms. Place like terms in columns. Combine like terms. Place like terms in columns. Example: Adding Polynomials Vertically

13. Add. A. (6x 2 + 6x + 13) + (3x 2 + 2x + 4) 6x 2 + 6x + 13 + 3x 2 + 2x + 4 9x 2 + 8x + 17 Combine like terms. Place like terms in columns. Try This

14. Add. B. (4mn 2 + 6m + 2n) + (2mn 2 – 2m – 2n) C. (x 2 y 2 – 5x 2 ) + (2y 2 – 2) + (x 2 ) + 2mn 2 – 2m – 2n 6mn 2 + 4m 4mn 2 + 6m + 2n Combine like terms. Place like terms in columns. 2y 2 – 2 + x 2 x 2 y 2 – 4x 2 + 2y 2 – 2 x 2 y 2 – 5x 2 Combine like terms. Place like terms in columns. Try This

15. 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. 1212 Example: Application

16. = 6b + 6h + 24 P = 2b + 2h + 12P = 4b + 4h + 12 P = (2b + 2h + 12) + (4b + 4h + 12) = 2b + 2h + 12 + 4b + 4h + 12 She will need 6b + 6h + 24 in. of wood. Combine like terms. Perimeter of photograph 1:Perimeter of photograph 2: Example Continued

17. 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. Try This

18. = 8b + 8h + 32 P = 2b + 2h + 16P = 6b + 6h + 16 P = (2b + 2h + 16) + (6b + 6h + 16) = 2b + 2h + 16 + 6b + 6h + 16 He will need 8b + 8h + 32 in. of wood. Combine like terms. Perimeter of photograph 1:Perimeter of photograph 2: Try This Continued

19. Add. 1. (2m 2 – 3m + 7) + (7m 2 – 1) 2. (yz 2 + 5yz + 7) + (2yz 2 – yz) 3. 9m 2 – 3m + 6 3yz 2 + 4yz + 7 7xy + 2x + 3y + 2 2 (2xy 2 + 2x – 6) + (5xy 2 + 3y + 8) Lesson Quiz: Part 1

20. 4. (3np 3 + 4n) (5np 3 – 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. 7x + 2y+ 4 8np 3 + 5n – 9 Lesson Quiz: Part 2