pre-algebra 13-3 adding polynomials pre-algebra homework page 680 #20-24
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Pre-Algebra
13-3 Adding Polynomials
Pre-Algebra HOMEWORK
Page 680
#20-24
Our Learning Goal
Students will be able to classify, simplify,
add and subtract polynomials.
Pre-Algebra
13-1 Polynomials
Students will be able to classify, simplify, add and subtract polynomials by completing the
following assignments.
•Learn to classify polynomials by degree and by
the number of terms.
•Learn to simplify polynomials.
•Learn to add polynomials.
•Learn to subtract polynomials. …..and that’s all folks!
Pre-Algebra
13-1 Polynomials
Today’s Learning Goal Assignment
Learn to add polynomials.
Pre-Algebra
13-3 Adding Polynomials
13-3 Adding Polynomials
Pre-Algebra
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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
Pre-Algebra
13-3 Adding Polynomials
44 ft26 m
7x2 – 3x + 1
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
Pre-Algebra
13-3 Adding Polynomials
Learn to add polynomials.
Pre-Algebra
13-3 Adding Polynomials
Additional Example 1A: Adding Polynomials Horizontally
Add.
A. (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.
Pre-Algebra
13-3 Adding Polynomials
Try This: Example 1A
Add.
A. (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.
Pre-Algebra
13-3 Adding Polynomials
Additional Example 1B: Adding Polynomials Horizontally
Add.
B. (6x3+ 8y2 + 5xy) + (4xy – 2y2)
(6x3+ 8y2+ 5xy) + (4xy – 2y2)
6x3 + 8y2 + 5xy + 4xy – 2y2
6x + 6y + 9xy3 2
Associative Property
Combine like terms.
Pre-Algebra
13-3 Adding Polynomials
Try This: Example 1B
Add.
B. (9x3 + 6p2 + 3xy) + (8xy – 3p2)
(9x + 6p + 3xy) + (8xy – 3p )3 2 2
9x + 6p + 3xy + 8xy – 3p 3 2 2
9x3+ 3p2+ 11xy
Associative Property
Combine like terms.
Pre-Algebra
13-3 Adding Polynomials
Additional Example 1C: Adding Polynomials Horizontally
Add.
C. (3x2y – 5x) + (4x + 7) + 6x2y
(3x2y – 5x) + (4x + 7) + 6x2y
9x2y – x + 7
Associative Property
Combine like terms.
3x2y – 5x + 4x + 7 + 6x2y
Pre-Algebra
13-3 Adding Polynomials
Try This: Example 1C
Add.
C. (3z2w – 5x) + (2x + 8) + 6z2w
(3z2w – 5x) + (2x + 8) + 6z2w
9z2w – 3x + 8
Associative Property
Combine like terms.
3z2w – 5x + 2x + 8 + 6z2w
Pre-Algebra
13-3 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.
Pre-Algebra
13-3 Adding Polynomials
Additional Example 2A: Adding Polynomials Vertically
Add.
A. (4x2 + 2x + 11) + (2x2 + 6x + 9)
4x2 + 2x + 11
+ 2x2 + 6x + 9
6x2 + 8x + 20
Pre-Algebra
13-3 Adding Polynomials
Combine like terms.
Place like terms in columns.
Try This: Example 2A
Add.
A. (6x2 + 6x + 13) + (3x2+ 2x + 4)
Pre-Algebra
13-3 Adding Polynomials
6x2 + 6x + 13
+ 3x2 + 2x + 4
9x2 + 8x + 17 Combine like terms.
Place like terms in columns.
Additional Example 2B & 2C: Adding Polynomials Vertically
Add.
B. (3mn2 – 6m + 6n) + (5mn2 + 2m – 6n)
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
Pre-Algebra
13-3 Adding Polynomials
Combine like terms.
Place like terms in columns.
Combine like terms.
Place like terms in columns.
Try This: Example 2B & 2C
Add.
B. (4mn2 + 6m + 2n) + (2mn2 – 2m – 2n)
C. (x2y2 – 5x2) + (2y2 – 2) + (x2)
Pre-Algebra
13-3 Adding Polynomials
+ 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.
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.
Pre-Algebra
13-3 Adding Polynomials
1 2
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:
Pre-Algebra
13-3 Adding Polynomials
Try This: 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.
Pre-Algebra
13-3 Adding Polynomials
Try This: 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:
Pre-Algebra
13-3 Adding Polynomials
Lesson Quiz: Part 1
Add.
1. (2m2 – 3m + 7) + (7m2 – 1)
2. (yz2 + 5yz + 7) + (2yz2 – yz)
3.
Insert Lesson Title Here
9m2 – 3m + 6
3yz2+ 4yz + 7
7xy + 2x + 3y + 22
Pre-Algebra
13-3 Adding Polynomials
(2xy2 + 2x – 6)
+ (5xy2 + 3y + 8)
Lesson Quiz: Part 2
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
Insert Lesson Title Here
8np3 + 5n – 9
Pre-Algebra
13-3 Adding Polynomials