combine like terms. 1. 9x + 4x2. –3y + 7y 3. 7n + (–8n) + 12n find the perimeter of each...
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Combine 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
Warm Up
Pre-Algebra
Adding Polynomials
13-3
Learn to add polynomials.
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.
Example: 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.
Example: 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
Example: Adding Polynomials Horizontally
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.
Try This
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.
Try This
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
Try This
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.
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.
Example: 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
Combine like terms.
Place like terms in columns.
Combine like terms.
Place like terms in columns.
Example: Adding Polynomials Vertically
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.
Try This
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.
Try This
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
Example: Application
= 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:
Example Continued
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.
Try This
= 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:
Try This Continued
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)
Lesson Quiz: Part 1
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
Lesson Quiz: Part 2