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Holt Algebra 1 7-6 Adding and Subtracting Polynomials 7-6 Adding and Subtracting Polynomials Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p 5p 4. 5n + 6n 2 Simplify each expression. 5. 3(x + 4) 6. 2(t + 3) 7. 1(x 2 4x 6) 6x6x 10y 3p3p not like terms 3x + 12 2t 6 x 2 + 4x + 6

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Add or Subtract.. Example 1: Adding and Subtracting Monomials A. 12p 3 + 11p 2 + 8p 3 12p 3 + 11p 2 + 8p 3 20p 3 + 11p 2 Identify like terms. Combine like terms. B. 5x 2 6 3x + 8 5x 2 6 3x + 8 5x 2 3x + 2 Identify like terms. Combine like terms.

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Add or Subtract.. Example 1: Adding and Subtracting Monomials C. t 2 + 2s 2 4t 2 s 2 t 2 + 2s 2 4t 2 s 2 3t 2 + s 2 Identify like terms. Combine like terms. D. 10m 2 n + 4m 2 n 8m 2 n 10m 2 n + 4m 2 n 8m 2 n 6m2n6m2n Identify like terms. Combine like terms.

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials You try these! a. 2s 2 + 3s 2 + s Add or subtract. Ans: 5s 2 + s b. 4z 4 8 + 16z 4 + 2 Ans: 20z 4 6

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials c. 2x 8 + 7y 8 x 8 y 8 Add or subtract. Ans: x 8 + 6y 8 d. 9b 3 c 2 + 5b 3 c 2 13b 3 c 2 Ans: b 3 c 2

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: In horizontal form, regroup and combine like terms. = (5x 2 + 2x 2 ) + (4x + 5x) + (1 + 2) = 7x 2 + 9x + 3 5x 2 + 4x + 1 + 2x 2 + 5x + 2 7x2 + 9x + 37x2 + 9x + 3 (5x 2 + 4x + 1) + (2x 2 + 5x + 2)

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Add. A. (4m 2 + 5) + (m 2 m + 6) Ans: 5m 2 m + 11 B. (10xy + x) + (3xy + y) Ans: 7xy + x + y

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Add. (6x 2 4y) + (3x 2 + 3y 8x 2 2y) Ans: x 2 3y

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Add.

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials You Try! Add (5a 3 + 3a 2 6a + 12a 2 ) + (7a 3 10a). Ans:12a 3 + 15a 2 16a

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Subtract. Subtracting Polynomials (x 3 + 4y) (2x 3 ) Ans: x 3 + 4y

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Subtract. (7m 4 2m 2 ) (5m 4 5m 2 + 8) Ans: 2m 4 + 3m 2 8

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Subtract. (10x 2 3x + 7) (x 2 9) Ans: 11x 2 3x + 16

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Subtract. (9q 2 3q) (q 2 5) Ans: 8q 2 3q + 5

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Subtract. (2x 2 3x 2 + 1) (x 2 + x + 1) Ans: 2x 2 x You Try!

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x 2 + 7x 5 and the area of plot B can be represented by 5x 2 4x + 11. Write a polynomial that represents the total area of both plots of land. (3x 2 + 7x 5)(5x 2 4x + 11) Plot A.Plot B. +

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Lesson Quiz: Part I Add or subtract. 1. 7m 2 + 3m + 4m 2 2. (r 2 + s 2 ) (5r 2 + 4s 2 ) 3. (10pq + 3p) + (2pq 5p + 6pq) 4. (14d 2 8) + (6d 2 2d +1) 5. (2.5ab + 14b) (1.5ab + 4b)

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Holt Algebra 1 7-6 Adding and Subtracting Polynomials Lesson Quiz: Part II 6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x 2 + 12x + 9, and the area of the second wall is modeled by 36x 2 12x + 1. Write a polynomial that represents the total area of the two walls.