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


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7 x 2 – 3 x + 1. Warm Up Combine like terms. 1. 9 x + 4 x 2. –3 y + 7 y 3. 7 n + (–8 n ) + 12 n 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(2 x 2 – x ) + x 2 + 1. 13 x. 4 y. 11 n. 44 ft. 26 m.

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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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Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

Learn to add and subtract polynomials.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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)


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

(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)


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

(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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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)


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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)


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

(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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

+ 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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

+ 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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

Subtraction is the opposite of addition. To

subtract a polynomial, you need to find its

opposite.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

To subtract a polynomial, add its opposite.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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.


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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)


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


Warm up combine like terms 1 9 x 4 x 2 3 y 7 y 3 7 n 8 n 12 n

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


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