1. Holt CA Course 1 12-3Adding Polynomials Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. Holt CA Course 1 12-3Adding 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. Holt CA Course 1 12-3Adding Polynomials Preview of Algebra 1 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1.3 California Standards

4. Holt CA Course 1 12-3Adding Polynomials Additional Example 1: Adding Polynomials Horizontally Add. A. (5x 3 + x 2 + 2) + (4x 3 + 6x 2 ) 5x 3 + x 2 + 2 + 4x 3 + 6x 2 Commutative PropertyCombine like terms.Write as one polynomial. 5x 3 + 4x 3 + x 2 + 6x 2 + 2 9x 3 + 7x 2 + 2

5. Holt CA Course 1 12-3Adding Polynomials Additional Example 1: Adding Polynomials Horizontally Add. B. (6x 3 + 8y 2 + 5xy) + (4xy – 2y 2 ) 6x 3 + 8y 2 + 5xy + 4xy – 2y 2 6x 3 + 8y 2 – 2y 2 + 5xy + 4xy 6x 3 + 6y 2 + 9xy Commutative PropertyCombine like terms.Write as one polynomial.

6. Holt CA Course 1 12-3Adding Polynomials Additional Example 1: Adding Polynomials Horizontally 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 Commutative PropertyCombine like terms. 3x 2 y + 6x 2 y – 5x + 4x + 7 Write as one polynomial.

7. Holt CA Course 1 12-3Adding Polynomials Check It Out! Example 1 Add. A. (3y 4 + y 2 + 6) + (5y 4 + 2y 2 ) 3y 4 + y 2 + 6 + 5y 4 + 2y 2 Commutative PropertyCombine like terms.Write as one polynomial. 3y 4 + 5y 4 + y 2 + 2y 2 + 6 8y 4 + 3y 2 + 6

8. Holt CA Course 1 12-3Adding Polynomials Check It Out! Example 1 Add. B. (9x 3 + 6p 2 + 3xy) + (8xy – 3p 2 ) Commutative PropertyCombine like terms.Write as one polynomial. 9x 3 + 6p 2 + 3xy + 8xy – 3p 2 9x 3 + 6p 2 – 3p 2 + 3xy + 8xy 9x 3 + 3p 2 + 11xy

9. Holt CA Course 1 12-3Adding Polynomials Check It Out! Example 1 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 Commutative PropertyCombine like terms. 3z 2 w + 6z 2 w – 5x + 2x + 8 Write as one polynomial.

10. Holt CA Course 1 12-3Adding Polynomials You can also add polynomials in a vertical format. Write the second polynomial below the first one. Be sure to line up the like terms. If the terms are rearranged, remember to keep the correct sign with each term.

11. Holt CA Course 1 12-3Adding 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.

12. Holt CA Course 1 12-3Adding 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.

13. Holt CA Course 1 12-3Adding 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.

14. Holt CA Course 1 12-3Adding 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.

15. Holt CA Course 1 12-3Adding 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

16. Holt CA Course 1 12-3Adding 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: P = 2w + 2l

17. Holt CA Course 1 12-3Adding 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.

18. Holt CA Course 1 12-3Adding 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: P = 2w + 2l

19. Holt CA Course 1 12-3Adding Polynomials Lesson Quiz Add. 1. (2m 2 – 3m + 7) + (7m 2 – 1) 2. (yz 2 + 5yz + 7) + (2yz 2 – yz) 3. (2xy 2 + 2x – 6) + (5xy 2 + 3y + 8) 9m 2 – 3m + 6 3yz 2 + 4yz + 7 7xy 2 + 2x + 3y + 2 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