# Algebra unit 8.1

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08-Jul-2015Category

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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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