Course 3

14-3 Adding Polynomials14-3 Adding Polynomials

Course 3

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 3

14-3 Adding Polynomials

Warm UpCombine like terms.

1. 9x + 4x 2. –3y + 7y3. 7n + (–8n) + 12n

Find the perimeter of each rectangle.

4. a 10 ft by 12 ft rectangle5. a 5 m by 8 m rectangle

Simplify.

6. 3(2x2 – x) + x2+ 1

13x 4y11n

44 ft26 m

7x2 – 3x + 1

Course 3

14-3 Adding Polynomials

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

Course 3

14-3 Adding Polynomials

Learn to add polynomials.

Course 3

14-3 Adding Polynomials

Additional Example 1A: Adding Polynomials Horizontally

Add.

(5x3 + x2 + 2) + (4x3 + 6x2)

(5x + x + 2) + (4x + 6x )3 2 3 2

5x + x + 2 + 4x + 6x 3 2 3 2

9x + 7x + 23 2

Associative Property

Combine like terms.

Course 3

14-3 Adding Polynomials

Additional Example 1B: Adding Polynomials Horizontally

Add.

(6x3+ 8y2 + 5xy) + (4xy – 2y2)

(6x3+ 8y2+ 5xy) + (4xy – 2y2)

6x3 + 8y2 + 5xy + 4xy – 2y2

6x + 6y + 9xy3 2

Associative Property

Combine like terms.

Course 3

14-3 Adding Polynomials

Additional Example 1C: Adding Polynomials Horizontally

Add.

(3x2y – 5x) + (4x + 7) + 6x2y

(3x2y – 5x) + (4x + 7) + 6x2y

9x2y – x + 7

Associative Property

Combine like terms.

3x2y – 5x + 4x + 7 + 6x2y

Course 3

14-3 Adding Polynomials

Check It Out: Example 1A

Add.

(3y4 + y2 + 6) + (5y4 + 2y2)

(3y + y + 6) + (5y + 2y )4 2 4 2

3y + y + 6 + 5y + 2y 4 2 4 2

8y + 3y + 64 2

Associative Property

Combine like terms.

Course 3

14-3 Adding Polynomials

Check It Out: Example 1B

Add.

(9x3 + 6p2 + 3xy) + (8xy – 3p2)

(9x + 6p2 + 3xy) + (8xy – 3p2)3

9x + 6p + 3xy + 8xy – 3p 3 2 2

9x3+ 3p2 + 11xy

Associative Property

Combine like terms.

Course 3

14-3 Adding Polynomials

Check It Out: Example 1C

Add.

(3z2w – 5x) + (2x + 8) + 6z2w

(3z2w – 5x) + (2x + 8) + 6z2w

9z2w – 3x + 8

Associative Property

Combine like terms.

3z2w – 5x + 2x + 8 + 6z2w

Course 3

14-3 Adding Polynomials

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.

Course 3

14-3 Adding Polynomials

Additional Example 2: Adding Polynomials Vertically

Add.

A. (4x2 + 2x + 11) + (2x2 + 6x + 9)

4x2 + 2x + 11

+ 2x2 + 6x + 9

6x2 + 8x + 20 Combine like terms.

Place like terms in columns.

Course 3

14-3 Adding Polynomials

Additional Example 2: Adding Polynomials Vertically

Add.

B. (3mn2 – 6m + 6n) + (5mn2 + 2m – n)

C. (–x2y2 + 5x2) + (–2y2 + 2) + (x2 + 8)

+ 5mn2 + 2m – n

8mn2 – 4m + 5n

–2y2 + 2

+ x2 + 8

–x2y2 + 6x2 – 2y2 + 10

3mn2 – 6m + 6n

–x2y2 + 5x2

Combine like terms.

Place like terms in columns.

Combine like terms.

Place like terms in columns.

Course 3

14-3 Adding Polynomials

Check It Out: Example 2

Add.

A. (6x2 + 6x + 13) + (3x2+ 2x + 4)

6x2 + 6x + 13

+ 3x2 + 2x + 4

9x2 + 8x + 17 Combine like terms.

Place like terms in columns.

Course 3

14-3 Adding Polynomials

Check It Out: Example 2

Add.

B. (4mn2 + 6m + 2n) + (2mn2 – 2m – 2n)

C. (x2y2 – 5x2) + (2y2 – 2) + (x2)

+ 2mn2 – 2m – 2n

6mn2 + 4m

4mn2 + 6m + 2n

Combine like terms.

Place like terms in columns.

2y2 – 2

+ x2

x2y2 – 4x2 + 2y2 – 2

x2y2 – 5x2

Combine like terms.

Place like terms in columns.

Course 3

14-3 Adding Polynomials

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.

1 2

Course 3

14-3 Adding Polynomials

Additional Example 3 Continued

= 6b + 6h + 24

P = 2b + 2h + 12 P = 4b + 4h + 12

P = (2b + 2h + 12) + (4b + 4h + 12)

= 2b + 2h + 12 + 4b + 4h + 12

She will need 6b + 6h + 24 in. of wood.

Combine like terms.

Perimeter of photograph 1: Perimeter of photograph 2:

Course 3

14-3 Adding Polynomials

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.

Course 3

14-3 Adding Polynomials

Check It Out: Example 3 Continued

= 8b + 8h + 32

P = 2b + 2h + 16 P = 6b + 6h + 16

P = (2b + 2h + 16) + (6b + 6h + 16)

= 2b + 2h + 16 + 6b + 6h + 16

He will need 8b + 8h + 32 in. of wood.

Combine like terms.

Perimeter of photograph 1: Perimeter of photograph 2:

Course 3

14-3 Adding Polynomials

Lesson Quiz: Part I

Add.

1. (2m2 – 3m + 7) + (7m2 – 1)

2. (yz2 + 5yz + 7) + (2yz2 – yz)

3.

9m2 – 3m + 6

3yz2+ 4yz + 7

7xy + 2x + 3y + 22

(2xy2 + 2x – 6) + (5xy2 + 3y + 8)

Course 3

14-3 Adding Polynomials

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

8np3 + 5n – 9