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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