Holt Algebra 1

7-6 Adding and Subtracting Polynomials7-6 Adding and Subtracting Polynomials

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Warm UpSimplify each expression by combining like terms.

1. 4x + 2x

2. 3y + 7y

3. 8p – 5p

4. 5n + 6n2

Simplify each expression.

5. 3(x + 4)

6. –2(t + 3)

7. –1(x2 – 4x – 6)

6x

10y

3p

not like terms

3x + 12

–2t – 6

–x2 + 4x + 6

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add and subtract polynomials.

Objective

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add or Subtract..

Example 1: Adding and Subtracting Monomials

A. 12p3 + 11p2 + 8p3

12p3 + 11p2 + 8p3

12p3 + 8p3 + 11p2

20p3 + 11p2

Identify 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.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add or Subtract..

Example 1: Adding and Subtracting Monomials

C. 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 – 8m2n

10m2n + 4m2n – 8m2n

6m2n

Identify like terms.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Like terms are constants or terms with the same variable(s) raised to the same power(s). To review combining like terms, see lesson 1-7.

Remember!

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Check It Out! Example 1

a. 2s2 + 3s2 + s

Add or subtract.

2s2 + 3s2 + s

5s2 + s

b. 4z4 – 8 + 16z4 + 2

4z4 – 8 + 16z4 + 2

4z4 + 16z4 – 8 + 2

20z4 – 6

Identify like terms.

Combine like terms.

Identify like terms.Rearrange terms so that

like terms are together.Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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.

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, use the Associative and Commutative Properties to regroup and combine like terms.

(5x2 + 4x + 1) + (2x2 + 5x + 2)

= (5x2 + 2x2) + (4x + 5x) + (1 + 2)

= 7x2 + 9x + 3

5x2 + 4x + 1+ 2x2 + 5x + 2

7x2 + 9x + 3

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add.

Example 2: Adding Polynomials

A. (4m2 + 5) + (m2 – m + 6)

(4m2 + 5) + (m2 – m + 6)

(4m2 + m2) + (–m) +(5 + 6)

5m2 – m + 11

Identify like terms.

Group like terms together.

Combine like terms.

B. (10xy + x) + (–3xy + y)

(10xy + x) + (–3xy + y)

(10xy – 3xy) + x + y

7xy + x + y

Identify like terms.

Group like terms together.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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. 6x2 – 4y+ –5x2 + y

x2 – 3y Simplify.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add.

Example 2D: Adding Polynomials

Identify like terms.

Group like terms together.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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 – 8

Rewrite subtraction as addition of the opposite.

Identify like terms.

Group like terms together.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3C: Subtracting Polynomials

(–10x2 – 3x + 7) – (x2 – 9)

(–10x2 – 3x + 7) + (–x2 + 9)

(–10x2 – 3x + 7) + (–x2 + 9)

–10x2 – 3x + 7–x2 + 0x + 9

–11x2 – 3x + 16

Rewrite subtraction as addition of the opposite.

Identify like terms.

Use the vertical method.Write 0x as a placeholder.Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3D: Subtracting Polynomials

(9q2 – 3q) – (q2 – 5)

(9q2 – 3q) + (–q2 + 5)

(9q2 – 3q) + (–q2 + 5)

9q2 – 3q + 0+ − q2 – 0q + 5

8q2 – 3q + 5

Rewrite subtraction as addition of the opposite.

Identify like terms.Use the vertical method.Write 0 and 0q as

placeholders.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Check It Out! Example 3

Subtract.

(2x2 – 3x2 + 1) – (x2 + x + 1)

(2x2 – 3x2 + 1) + (–x2 – x – 1)

(2x2 – 3x2 + 1) + (–x2 – x – 1)

–x2 + 0x + 1 + –x2 – x – 1–2x2 – x

Rewrite subtraction as addition of the opposite.

Identify like terms.

Use the vertical method.Write 0x as a placeholder.

Combine like terms.

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 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)

8x2 + 3x + 6

Plot A.Plot B.

Combine like terms.

+

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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 – 1500 Eastern plant profit.

–0.02x2 + 21x – 1700 Southern plant profit.Combine like terms.

+–0.05x2 + 46x – 3200

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Lesson Quiz: Part I

Add 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 + 3m

18pq – 2p

20d2 – 2d – 7

5. (2.5ab + 14b) – (–1.5ab + 4b) 4ab + 10b

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 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