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Unit 8.1

### Transcript of Algebra unit 8.1

• UNIT 8.1 ADDING AND SUBTRACTINGPOLYNOMIALS

• Warm UpSimplify each expression by combining like terms.1. 4x + 2x2. 3y + 7y3. 8p 5p4. 5n + 6n2

Simplify each expression.5. 3(x + 4)6. 2(t + 3)7. 1(x2 4x 6)6x10y3pnot like terms3x + 122t 6x2 + 4x + 6

• Add and subtract polynomials. Objective

• Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

• Add or Subtract..Example 1: Adding and Subtracting MonomialsA. 12p3 + 11p2 + 8p3 12p3 + 11p2 + 8p3 12p3 + 8p3 + 11p2 20p3 + 11p2Identify like terms.Rearrange terms so that like terms are together.Combine like terms.B. 5x2 6 3x + 8 5x2 6 3x + 8 5x2 3x + 8 6 5x2 3x + 2 Identify like terms.Rearrange terms so that like terms are together.Combine like terms.

• Add or Subtract..Example 1: Adding and Subtracting MonomialsC. t2 + 2s2 4t2 s2 t2 4t2 + 2s2 s2 t2 + 2s2 4t2 s2 3t2 + s2 Identify like terms.Rearrange terms so that like terms are together.Combine like terms.D. 10m2n + 4m2n 8m2n10m2n + 4m2n 8m2n6m2nIdentify like terms.Combine like terms.

• Check It Out! Example 1 a. 2s2 + 3s2 + s Add or subtract. 2s2 + 3s2 + s 5s2 + s b. 4z4 8 + 16z4 + 24z4 8 + 16z4 + 24z4 + 16z4 8 + 220z4 6 Identify like terms.Combine like terms.Identify like terms.Rearrange terms so that like terms are together.Combine like terms.

• Check It Out! Example 1 c. 2x8 + 7y8 x8 y8 Add or subtract.2x8 + 7y8 x8 y8 2x8 x8 + 7y8 y8 x8 + 6y8 d. 9b3c2 + 5b3c2 13b3c2 9b3c2 + 5b3c2 13b3c2 b3c2 Identify like terms.Combine like terms.Identify like terms.Rearrange terms so that like terms are together.Combine like terms.

• Polynomials can be added in either vertical or horizontal form.In vertical form, align the like terms and add:In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.(5x2 + 4x + 1) + (2x2 + 5x + 2)= (5x2 + 2x2 + 1) + (4x + 5x) + (1 + 2)= 7x2 + 9x + 3

• Add.Example 2: Adding PolynomialsA. (4m2 + 5) + (m2 m + 6) (4m2 + 5) + (m2 m + 6) (4m2 + m2) + (m) +(5 + 6)5m2 m + 11Identify like terms.Group like terms together.Combine like terms.B. (10xy + x) + (3xy + y)(10xy + x) + (3xy + y)(10xy 3xy) + x + y7xy + x + yIdentify like terms.Group like terms together.Combine like terms.

• Add.Example 2C: Adding Polynomials (6x2 4y) + (3x2 + 3y 8x2 2y)Identify like terms.Group like terms together within each polynomial.Combine like terms.(6x2 4y) + (3x2 + 3y 8x2 2y) (6x2 + 3x2 8x2) + (3y 4y 2y)Use the vertical method.x2 3ySimplify.

• Add.Example 2D: Adding PolynomialsIdentify like terms.Group like terms together.Combine like terms.

• Check It Out! Example 2 Add (5a3 + 3a2 6a + 12a2) + (7a3 10a).(5a3 + 3a2 6a + 12a2) + (7a3 10a)(5a3 + 7a3) + (3a2 + 12a2) + (10a 6a)12a3 + 15a2 16a Identify like terms.Group like terms together.Combine like terms.

• To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial:(2x3 3x + 7)= 2x3 + 3x 7

• Subtract.Example 3A: Subtracting Polynomials(x3 + 4y) (2x3)(x3 + 4y) + (2x3)(x3 + 4y) + (2x3)(x3 2x3) + 4y x3 + 4y Rewrite subtraction as addition of the opposite.Identify like terms.Group like terms together.Combine like terms.

• Subtract.Example 3B: Subtracting Polynomials(7m4 2m2) (5m4 5m2 + 8)(7m4 2m2) + (5m4 + 5m2 8)(7m4 5m4) + (2m2 + 5m2) 8(7m4 2m2) + (5m4 + 5m2 8)2m4 + 3m2 8Rewrite subtraction as addition of the opposite.Identify like terms.Group like terms together.Combine like terms.

• Subtract.Example 3C: Subtracting Polynomials(10x2 3x + 7) (x2 9)(10x2 3x + 7) + (x2 + 9)(10x2 3x + 7) + (x2 + 9)11x2 3x + 16Rewrite subtraction as addition of the opposite.Identify like terms.Use the vertical method.Write 0x as a placeholder.Combine like terms.

• Subtract.Example 3D: Subtracting Polynomials (9q2 3q) (q2 5) (9q2 3q) + (q2 + 5) (9q2 3q) + (q2 + 5)8q2 3q + 5Rewrite subtraction as addition of the opposite.Identify like terms.Use the vertical method.Write 0 and 0q as placeholders.Combine like terms.

• Check It Out! Example 3 Subtract.(2x2 3x2 + 1) (x2 + x + 1)(2x2 3x2 + 1) + (x2 x 1)(2x2 3x2 + 1) + (x2 x 1)2x2 xRewrite subtraction as addition of the opposite.Identify like terms.Use the vertical method.Write 0x as a placeholder.Combine like terms.

• 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 3x2 + 7x 5 and the area of plot B can be represented by 5x2 4x + 11. Write a polynomial that represents the total area of both plots of land. Example 4: Application(3x2 + 7x 5)(5x2 4x + 11)Plot A.Plot B.Combine like terms.+

• Check It Out! Example 4 The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant.Use the information above to write a polynomial that represents the total profits from both plants.0.03x2 + 25x 1500Eastern plant profit.0.02x2 + 21x 1700Southern plant profit.Combine like terms.+

• Lesson Quiz: Part IAdd or subtract.1. 7m2 + 3m + 4m2 2. (r2 + s2) (5r2 + 4s2)3. (10pq + 3p) + (2pq 5p + 6pq)4. (14d2 8) + (6d2 2d +1)

(4r2 3s2)11m2 + 3m18pq 2p20d2 2d 7 5. (2.5ab + 14b) (1.5ab + 4b)4ab + 10b

• Lesson Quiz: Part II6. 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 4x2 + 12x + 9, and the area of the second wall is modeled by 36x2 12x + 1. Write a polynomial that represents the total area of the two walls.40x2 + 10

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