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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 nPowerPoint Presentation

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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Lesson Quiz for Student Response Systems Write the second polynomial below the first one, lining up the like terms.

7x2 – 3x + 1

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

Learn to add and subtract polynomials.

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

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)

(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.

4 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.x2 + 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.

+ 5 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.mn2 + 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.

6 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.x2 + 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.

+ 2 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.mn2 – 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 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.

subtract a polynomial, you need to find its

opposite.

Example 1: Finding the Opposite of a Polynomial 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.

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 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.

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. 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.

Example 1: Subtracting Polynomials Horizontally 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.

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 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.

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 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.

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 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.

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 Write the second polynomial below the first one, lining up the like terms.

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 Write the second polynomial below the first one, lining up the like terms.

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 Write the second polynomial below the first one, lining up the like terms.

Subtract.

(6a4– 3a2–8) – (–2a4 + 7)

(6a4– 3a2–8)

6a4– 3a2–8

– (–2a4 + 7)

+ 2a4– 7

Rearrange as needed.

8a4 – 3a2– 15

Lesson Quizzes Write the second polynomial below the first one, lining up the like terms.

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

9 Write the second polynomial below the first one, lining up the like terms.m2 – 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 Write the second polynomial below the first one, lining up the like terms.

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 Write the second polynomial below the first one, lining up the like terms.

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 Write the second polynomial below the first one, lining up the like terms.

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 Write the second polynomial below the first one, lining up the like terms.

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

3. Subtract.

(11p2 –5p + 9) – (3p2 + p – 17)

A. 14p2 +4p – 8

B. 14p2 –6p + 26

C. 8p2 –6p + 26

D.8p2 +4p – 8

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