Warm Up

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Warm Up Combine like terms. 1. 9x 4x 2. 3y
7y 3. 7n (8n) 12n Find the perimeter of
each rectangle. 4. a 10 ft by 12 ft rectangle 5.
a 5 m by 8 m rectangle Simplify. 6. 3(2x2 x)
x2 1
13x
4y
11n
44 ft
26 m
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Learn to add and subtract polynomials.
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Example 1A Adding Polynomials Horizontally Add. (
5x3 x2 2) (4x3 6x2)
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Example 1B Adding Polynomials Horizontally Add. (
6x3 8y2 5xy) (4xy 2y2)
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Example 1C Adding Polynomials Horizontally Add. (
3x2y 5x) (4x 7) 6x2y
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Example 2A Add. (3y4 y2 6) (5y4 2y2)
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Example 2B Add. (9x3 6p2 3xy) (8xy
3p2)
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Example 2C Add. (3z2w 5x) (2x 8) 6z2w
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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.
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Example 3 Adding Polynomials Vertically Add. A.
(4x2 2x 11) (2x2 6x 9)
Place like terms in columns.
Combine like terms.
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Example 3 Adding Polynomials Vertically Add. B.
(3mn2 6m 6n) (5mn2 2m n) C. (x2y2
5x2) (2y2 2) (x2 8)
Place like terms in columns.
Combine like terms.
x2y2 5x2
Place like terms in columns.
x2 8
Combine like terms.
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Example 4 Add. A. (6x2 6x 13) (3x2 2x
4)
Place like terms in columns.
Combine like terms.
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Example 4 Add. B. (4mn2 6m 2n) (2mn2 2m
2n) C. (x2y2 5x2) (2y2 2) (x2)
Place like terms in columns.
Combine like terms.
x2y2 5x2
Place like terms in columns.
x2
Combine like terms.
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Subtraction is the opposite of addition. To
subtract a polynomial, you need to find
its opposite.
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Example 1 Finding the Opposite of a Polynomial
Find the opposite of each polynomial.
A. 8x3y4z2
(8x3y4z2)
Distributive Property.
8x3y4z2
B. 3x4 8x2
(3x4 8x2)
Distributive Property.
3x4 8x2
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Additional Example 1 Finding the Opposite of a
Polynomial
Find the opposite of the polynomial.
C. 9a6b4 a4b2 1
(9a6b4 a4b2 1)
Distributive Property.
9a6b4 a4b2 1
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To subtract a polynomial, add its opposite.
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Example 1 Subtracting Polynomials Horizontally
Subtract.
A. (5x2 2x 3) (3x2 8x 4)
Add the opposite.
(5x2 2x 3) (3x2 8x 4)
Associative property.
5x2 2x 3 3x2 8x 4
2x2 6x 1
Combine like terms.
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Example 1 Subtracting Polynomials Horizontally
Subtract.
B. (b2 4b 1) (7b2 b 1)
Add the opposite.
(b2 4b 1) (7b2 b 1)
Associative property.
b2 4b 1 7b2 b 1
6b2 5b
Combine like terms.
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Example 2A
Subtract.
(2y3 3y 5) (4y3 3y 5)
Add the opposite.
(2y3 3y 5) (4y3 3y 5)
Associative property.
2y3 3y 5 4y3 3y 5
2y3
Combine like terms.
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Example 2B
Subtract.
(c3 2c2 3) (4c3 c2 1)
(c3 2c2 3) (4c3 c2 1)
Add the opposite.
c3 2c2 3 4c3 c2 1
Associative property.
3c3 3c2 4
Combine like terms.
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You can also subtract polynomials in a vertical
format. Write the second polynomial below the
first one, lining up the like terms.
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Example 3 Subtracting Polynomials Vertically
Subtract.
(2n2 4n 9) (6n2 7n 5)
(2n2 4n 9)
2n2 4n 9
(6n2 7n 5)
6n2 7n 5
Add the opposite.
4n2 3n 4
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Example 4 Subtracting Polynomials Vertically
Subtract.
(10x2 2x 7) (x2 5x 1)
(10x2 2x 7)
10x2 2x 7
(x2 5x 1)
x2 5x 1
Add the opposite.
9x2 3x 8
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Example 5 Subtracting Polynomials Vertically
Subtract.
(6a4 3a2 8) (2a4 7)
(6a4 3a2 8)
6a4 3a2 8
(2a4 7)
2a4 7
Rearrange as needed.
8a4 3a2 15
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz Part I
Add. 1. (2m2 3m 7) (7m2 1) 2. (yz2
5yz 7) (2yz2 yz) 3.
(2xy2 2x 6)
(5xy2 3y 8)
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Lesson Quiz
Find the opposite of each polynomial.
Subtract. 3. (3z2 7z 6) (2z2 z
12)
2. 3m3 2m2n
3m3 2m2n
1. 3a2b2c3
3a2b2c3
z2 8z 18
4. 18h3 (4h3 h2 12h 2) 5. (3b2c 5bc2
8b2) (4b2c 2bc2 c2)
22h3 h2 12h 2
b2c 3bc2 8b2 c2
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Lesson Quiz for Student Response Systems
1. Add (4p2 8p 11) (6p2 9). A. 10p2 8p
2 B. 10p2 8p 20 C. 2p2 8p
2 D. 10p2 8p 20
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Lesson Quiz for Student Response Systems
2. Add (gh2 9gh 11) (3gh2 gh). A. 2gh2
8gh 11 B. 2gh2 10gh 11 C. 4gh2
8gh 11 D. 4gh2 10gh 11
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Lesson Quiz for Student Response Systems
3. Add (7uv3 11u) (6uv3 u 9) (4u
2). A. 13uv3 6u 7 B. uv2 16u 7
C. uv3 14u 11 D. 13uv3 14u 11
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Lesson Quiz for Student Response Systems
3. Subtract. (11p2 5p 9) (3p2 p 17)
A. 14p2 4p 8 B. 14p2 6p 26 C.
8p2 6p 26 D. 8p2 4p 8