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Warm Up Combine like terms. 1. 9 x + 4 x 2. –3 y + 7 y 3. 7 n + (–8 n ) + 12 n

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7x2 – 3x + 1

Warm Up

Combine like terms.

1.9x + 4x2. –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

Learn to add and subtract polynomials.

2

3

2

3

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

2

3

2

3

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

2

3

9x + 7x + 2

Associative Property

Combine like terms.

Example 1A: Adding Polynomials Horizontally

Add.

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

(6x3+ 8y2+ 5xy) + (4xy – 2y2)

6x3 + 8y2 + 5xy + 4xy – 2y2

2

3

6x + 6y + 9xy

Associative Property

Combine like terms.

Example 1B: Adding Polynomials Horizontally

Add.

(6x3+ 8y2 + 5xy) + (4xy – 2y2)

(3x2y – 5x) + (4x + 7) + 6x2y

3x2y – 5x + 4x + 7 + 6x2y

9x2y – x + 7

Associative Property

Combine like terms.

Example 1C: Adding Polynomials Horizontally

Add.

(3x2y – 5x) + (4x + 7) + 6x2y

2

4

2

4

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

2

4

2

4

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

2

4

8y + 3y + 6

Associative Property

Combine like terms.

Example 2A

Add.

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

3

(9x + 6p2 + 3xy) + (8xy – 3p2)

2

2

3

9x + 6p + 3xy + 8xy – 3p

9x3+ 3p2 + 11xy

Associative Property

Combine like terms.

Example 2B

Add.

(9x3 + 6p2 + 3xy) + (8xy – 3p2)

(3z2w – 5x) + (2x + 8) + 6z2w

3z2w – 5x + 2x + 8 + 6z2w

9z2w – 3x + 8

Associative Property

Combine like terms.

Example 2C

Add.

(3z2w – 5x) + (2x + 8) + 6z2w

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.

4x2 + 2x + 11

+ 2x2 + 6x + 9

6x2 + 8x + 20

Example 3: Adding Polynomials Vertically

Add.

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

Place like terms in columns.

Combine like terms.

+ 5mn2 + 2m – n

8mn2 – 4m + 5n

3mn2 – 6m + 6n

–2y2 + 2

–x2y2+ 6x2 – 2y2 + 10

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.

6x2 + 6x + 13

+ 3x2 + 2x + 4

9x2 + 8x + 17

Example 4

Add.

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

Place like terms in columns.

Combine like terms.

+ 2mn2 – 2m – 2n

6mn2 + 4m

4mn2 + 6m + 2n

2y2 – 2

x2y2– 4x2 + 2y2 – 2

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.

Subtraction is the opposite of addition. To

subtract a polynomial, you need to find its

opposite.

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

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

To subtract a polynomial, add its opposite.

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.

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.

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.

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.

You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms.

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

Example 4: Subtracting Polynomials Vertically

Subtract.

(10x2 + 2x –7) – (x2 + 5x + 1)

(10x2 + 2x –7)

10x2 + 2x –7

Add the

opposite.

– (x2 + 5x + 1)

+ –x2– 5x– 1

9x2– 3x– 8

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

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

9m2 – 3m + 6

3yz2+ 4yz + 7

2

7xy + 2x + 3y + 2

Lesson Quiz: Part I

Add.

1. (2m2 – 3m + 7) + (7m2 – 1)

2. (yz2 + 5yz + 7) + (2yz2 – yz)

3.

(2xy2 + 2x – 6)

+ (5xy2 + 3y + 8)

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

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

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

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

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