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14-3

Adding Polynomials. 14-3. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 7 x 2 – 3 x + 1. Warm Up Combine like terms. 1. 9 x + 4 x 2. –3 y + 7 y 3. 7 n + (–8 n ) + 12 n Find the perimeter of each rectangle. 4. a 10 ft by 12 ft rectangle

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14-3

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

  2. 7x2 – 3x + 1 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

  3. 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. Learn to add polynomials.

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

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

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

  8. 2 4 2 4 (3y + y + 6) + (5y + 2y ) 2 4 2 4 3y + y + 6 + 5y + 2y 2 4 8y + 3y + 6 Associative Property Combine like terms. Check It Out: Example 1A Add. (3y4 + y2 + 6) + (5y4 + 2y2)

  9. 3 (9x + 6p2 + 3xy) + (8xy – 3p2) 2 2 3 9x + 6p + 3xy + 8xy – 3p 9x3+ 3p2 + 11xy Associative Property Combine like terms. Check It Out: Example 1B Add. (9x3 + 6p2 + 3xy) + (8xy – 3p2)

  10. (3z2w – 5x) + (2x + 8) + 6z2w 3z2w – 5x + 2x + 8 + 6z2w 9z2w – 3x + 8 Associative Property Combine like terms. Check It Out: Example 1C Add. (3z2w – 5x) + (2x + 8) + 6z2w

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

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

  14. 6x2 + 6x + 13 + 3x2 + 2x + 4 9x2 + 8x + 17 Check It Out: Example 2 Add. A. (6x2 + 6x + 13) + (3x2+ 2x + 4) Place like terms in columns. Combine like terms.

  15. + 2mn2 – 2m – 2n 6mn2 + 4m 4mn2 + 6m + 2n 2y2 – 2 x2y2– 4x2 + 2y2 – 2 Check It Out: Example 2 Add. B. (4mn2 + 6m + 2n) + (2mn2 – 2m – 2n) C. (x2y2 – 5x2) + (2y2 – 2) + (x2) Place like terms in columns. Combine like terms. x2y2 – 5x2 Place like terms in columns. + x2 Combine like terms.

  16. 1 2 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.

  17. 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 + 12 + 4b + 4h + 12 = 6b + 6h + 24 Combine like terms. She will need 6b + 6h + 24 in. of wood.

  18. 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. Check It Out: 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 + 16 + 6b + 6h + 16 = 8b + 8h + 32 Combine like terms. He will need 8b + 8h + 32 in. of wood.

  20. 9m2 – 3m + 6 3yz2+ 4yz + 7 2 7xy + 2x + 3y + 2 Lesson Quiz: Part I Add. 1. (2m2 – 3m + 7) + (7m2 – 1) 2. (yz2 + 5yz + 7) + (2yz2 – yz) 3. (2xy2 + 2x – 6) + (5xy2 + 3y + 8)

  21. 8np3 + 5n – 9 Lesson Quiz: Part II 4. (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. 7x + 2y + 4

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