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Page 1: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM
Page 2: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

Page 3: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM
Page 4: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM
Page 5: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM
Page 6: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

• •

• •

Page 7: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

𝑥 𝑥2 5𝑦5

3𝑥 − 2 − 4𝑥 + 47𝑥 + 2 𝑥

−4𝑥7𝑦 − 𝑦

7

3𝑥 3𝑥2

3𝑥 − 2 − 4𝑥 + 4

• 4𝑥 − 3 4𝑥 − 3

3𝑥 + 10 3𝑥 + 10

𝑥 + 1

5 5𝑎 −5𝑏2 −5𝑎

𝑎2 −5 9𝑎 −9

9𝑏2 9 −9𝑎 5𝑏

3𝑥3𝑥2

Page 8: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

3𝑥 𝑥

2 3 + 𝑥 ≡ 6 + 2𝑥

9 − 6𝑥

9 − 6𝑥 ≡ 3(3 − 2𝑥)

3 3 + b , 𝑎 3 + 𝑏 , 𝑎 3 − 𝑏 , 𝑎 𝑎 + 𝑏 , 𝑎(3 − 𝑎)•

3 15

3 × 2 15 × 2

3𝑎 15𝑎

3 9

3 32

𝑥 𝑥2

24 36

2 × 3 × 4 3 × 3 × 4

2𝑥𝑦 3𝑥𝑦

3 𝑥

2 6 2𝑥

3 + 𝑥

2 6 + 2𝑥

Page 9: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

8 × 7 =(3 + 5)(2 + 5)

(𝑥 + 1)2

𝑥 + 1 𝑥 + 1

(2 + 𝑥)(3 − 𝑥)

2 + 𝑥 3 − 𝑥 ≡ 6 + 3𝑥 − 2𝑥 − 𝑥2

2 + 𝑥 3 − 𝑥 ≡ 6 + 𝑥 − 𝑥2

4𝑥

3 𝑥

2 6 2𝑥

𝑥 3𝑥 𝑥2

3 5

2 6 10

5 15 25

3 𝑥

2 6 2𝑥

5 15 5𝑥

56

8

7

(2 + 𝑥

(3 − 𝑥)

𝑥 + 1

𝑥 + 1𝑥 − 1

𝑥 − 1

Page 10: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

4(𝑥 + 𝑦) 𝑃 = 4(𝑥 + 𝑦)

4 𝑥 + 𝑦 ≡ 4𝑥 + 4𝑦

4 𝑥 + 𝑦 = 16

Page 11: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

𝑥2 𝑥3

2𝑥2 + 3𝑥2 ≡ 5𝑥2 5𝑥4𝑥2 𝑥3

𝑥2

𝑥3

2𝑥3 + 5𝑥2 7𝑥5

2𝑎 × 3𝑎𝑏, 𝑎2𝑐 × 𝑎𝑏

2𝑐2 + 3𝑐2 ≡ 5𝑐2

7𝑦3 − 𝑦3 ≡ 78𝑥2 − 6𝑥2 − 2𝑥2 ≡ 0𝑥2

5𝑔3 − 4𝑔3 ≡ 1𝑔3

Page 12: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

26 × 22 ≠ 212

23 × 34 ≠67

𝑎 𝑎1

0

• 39 × 38 86 ÷ 85

4? × 4? = 4100 4? × 4? = 4? × 4? × 4?

6 ÷ 3 = 2, so46 ÷ 43 = 42

35 × 32 = 97

72 × 74

= 7 × 7 × 7 × 7 × 7 × 7= 7?

34 ÷ 32

=3 × 3 × 3 × 3

3 × 3= 3?

Page 13: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

−3𝑥 − −3𝑥 −5𝑦 + 3𝑥 − −5𝑦 + 6𝑥(ℎ)

(𝑗)

2ℎ = 10

𝑥 + 𝑦 = 8, 𝑥 𝑦

𝑥 𝑦𝑥 𝑦

𝑥 − 𝑦 = 4𝑥 𝑦

19

ℎ ℎ ℎ 𝑗 𝑗

9

ℎ 𝑗 𝑗ℎ + 2𝑗 = 9

3ℎ + 2𝑗 = 19

3𝑦 − 2𝑥 = 102𝑦 – 2𝑥 = 6

Page 14: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

×

𝑥2 + 3𝑥 + 2

𝑥2 +2𝑥 − 8

(𝑥 + 2)

(𝑥 + 1)

Page 15: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

Page 16: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

Page 17: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

𝑛 = 1

10 − 𝑛 𝑛2

• 𝑛 = 1, 2, 3 100•

100

𝑛

𝑛2 + 1 2𝑛2 + 1

𝑛 + 7

1 2

7 14 21 28

0 7 14 21

1 8 15 22

8 9 10 11

2𝑛 + 1

Page 18: PowerPoint Presentation...8 2−6 2−2 2≡0 2 ... PowerPoint Presentation Author: test Created Date: 2/11/2020 3:17:15 PM

+ 4𝑛 + 𝑛 + 4

𝑛 + 4 4𝑛𝑛

𝑛

𝑛2𝑛 + 1

+1

𝑛

𝑛

4

4𝑛 4𝑛 + 3 4𝑛 − 1 4𝑛 + 7

4 7 10 13

1 4 7 10

30 27 24 21