1. Course 3 14-3 Adding Polynomials 14-3 Adding Polynomials Course 3 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Course 3 14-3 Adding Polynomials Warm Up 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

3. Course 3 14-3 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

4. Course 3 14-3 Adding Polynomials Learn to add polynomials.

5. Course 3 14-3 Adding Polynomials Additional Example 1A: Adding Polynomials Horizontally Add. (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.

6. Course 3 14-3 Adding Polynomials Additional Example 1B: Adding Polynomials Horizontally Add. (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.

7. Course 3 14-3 Adding Polynomials Additional Example 1C: Adding Polynomials Horizontally Add. (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

8. Course 3 14-3 Adding Polynomials Check It Out: Example 1A Add. (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.

9. Course 3 14-3 Adding Polynomials Check It Out: Example 1B Add. (9x 3 + 6p 2 + 3xy) + (8xy – 3p 2 ) (9x + 6p 2 + 3xy) + (8xy – 3p 2 ) 3 9x + 6p + 3xy + 8xy – 3p 3 2 2 9x 3 + 3p 2 + 11xy Associative PropertyCombine like terms.

10. Course 3 14-3 Adding Polynomials Check It Out: Example 1C Add. (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

11. Course 3 14-3 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.

12. Course 3 14-3 Adding Polynomials Additional Example 2: Adding Polynomials Vertically 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.

13. Course 3 14-3 Adding Polynomials Additional Example 2: Adding Polynomials Vertically Add. B. (3mn 2 – 6m + 6n) + (5mn 2 + 2m – n) 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.

14. Course 3 14-3 Adding Polynomials Check It Out: Example 2 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.

15. Course 3 14-3 Adding Polynomials Check It Out: Example 2 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.

16. Course 3 14-3 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. 1212

17. Course 3 14-3 Adding Polynomials Additional Example 3 Continued = 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:

18. Course 3 14-3 Adding Polynomials Check It Out: 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.

19. Course 3 14-3 Adding Polynomials Check It Out: Example 3 Continued = 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:

20. Course 3 14-3 Adding Polynomials Lesson Quiz: Part I 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)

21. Course 3 14-3 Adding Polynomials Lesson Quiz: Part II 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