Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a...
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Transcript of Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a...
![Page 1: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/1.jpg)
![Page 3: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/3.jpg)
Simplify Expressions with Multiplication
A. Simplify (–2a3b)(–5ab4).
(–2a3b)(–5ab4) = (–2 ● a ● a ● a ● b) ● (–5 ● a ● b ● b ● b ● b)
Definition of exponents
= –2(–5) ● a ● a ● a ● a ● b ● b ● b ● b ● b
Commutative Property
= 10a4b5 Definition of exponents
Answer: 10a4b5
![Page 4: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/4.jpg)
Simplify Expressions with Multiplication
B. Simplify (3a5)(c–2)(–2a–4b3).
(3a5)(c–2)(–2a–4b3)
Definition of negative exponents
Definition of exponents
![Page 5: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/5.jpg)
Simplify Expressions with Multiplication
Cancel out common factors.
Definition of exponents and fractions
Answer:
![Page 6: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/6.jpg)
A. A
B. B
C. C
D. D
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A. Simplify (–3x2y)(5x3y5).
A. –15x5y6
B. –15x6y5
C. 15x5y6
D.
![Page 10: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/10.jpg)
Simplify Expressions with Division
Answer:
Remember that a simplified expression cannot contain negative exponents.
Subtract exponents.
![Page 13: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/13.jpg)
Simplify Expressions with Powers
A. Simplify (–3c2d5)3.
(–3c2d5)3 = (–3)3(c2)3(d5)3 Power of a power
= –27c6d15 Simplify.
Answer: –27c6d15
![Page 14: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/14.jpg)
Simplify Expressions with Powers
Power of a product
Power of a quotient
B.
(–2)5 = –32
Answer:
![Page 15: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/15.jpg)
1. A
2. B
3. C
4. D
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A B C D
A. Simplify (x3)5.
A. x15
B. x8
C. x2
D.
![Page 17: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/17.jpg)
Method 1 Raise the numerator and the denominator to the fifth power before simplifying.
Simplify Expressions Using Several Properties
![Page 19: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/19.jpg)
Method 2 Simplify the fraction before raising to the fifth power.
Simplify Expressions Using Several Properties
![Page 22: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/22.jpg)
BIOLOGY There are about 5 × 106 red blood cells in one milliliter of blood. A certain blood sample contains 8.32 × 106 red blood cells. About how many milliliters of blood are in the sample?
Divide the number of red blood cells in the sample by the number of red blood cells in 1 milliliter of blood.
Answer: There are about 1.66 milliliters of blood in the sample.
← number of red blood cells in sample← number of red blood cells in 1 milliliter
![Page 23: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/23.jpg)
A. A
B. B
C. C
D. D
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A. 2
B. 20
C. 2 × 102
D. 2.592 × 1013
BIOLOGY A petri dish started with 3.6 × 105 germs in it. A half hour later, there are 7.2 × 107. How many times as great is the amount a half hour later?
![Page 25: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/25.jpg)
Simplify Polynomials
A. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2).
(2a3 + 5a – 7) – (a3 – 3a + 2)
= a3 + 8a – 9 Combine like terms.
Group like terms.
Distribute the –1.
Answer: a3 + 8a – 9
![Page 26: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/26.jpg)
Simplify Polynomials
B. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6).
(4x2 – 9x + 3) + (–2x2 – 5x – 6)
= 2x2 – 14x – 3 Combine like terms.
Remove parentheses.
Group like terms.
Answer: 2x2 – 14x – 3
![Page 27: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/27.jpg)
1. A
2. B
3. C
4. D
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A B C D
A. 7x2 + 3x – 8
B. –x2 + 3x – 8
C. –x2 + 3x + 2
D. –x2 + x + 2
A. Simplify (3x2 + 2x – 3) – (4x2 + x – 5).
![Page 28: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/28.jpg)
1. A
2. B
3. C
4. D
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A B C D
A. 9x2 + 6x + 7
B. –7x2 – 5x + 6
C. 3x2 – 6x + 7
D. 3x2 – 2x + 6
B. Simplify (–3x2 – 4x + 1) – (4x2 + x – 5).
![Page 29: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/29.jpg)
Simplify Using the Distributive Property
Find –y(4y2 + 2y – 3).
–y(4y2 + 2y – 3) = –y(4y2) –y(2y) – y(–3) Distributive Property
= –4y3 – 2y2 + 3yMultiply the monomials.
Answer: –4y3 – 2y2 + 3y
![Page 30: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/30.jpg)
1. A
2. B
3. C
4. D
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A B C D
A. –3x2 – 2x + 5
B. –4x4 – 3x2 – 6x
C. –3x4 + 2x2 – 5x
D. –3x4 – 2x3 + 5x
Find –x(2x3 – 2x + 5).
![Page 31: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/31.jpg)
Find (a2 + 3a – 4)(a + 2).
(a2 + 3a – 4)(a + 2)
= a3 + 5a2 + 2a – 8 Combine like terms.
Multiply Polynomials
Distributive Property
Distributive Property
Multiply monomials.
Answer: a3 + 5a2 + 2a – 8
![Page 32: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/32.jpg)
A. A
B. B
C. C
D. D
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A. x3 + 7x2 + 10x – 8
B. x2 + 4x + 2
C. x3 + 3x2 – 2x + 8
D. x3 + 7x2 + 14x – 8
Find (x2 + 3x – 2)(x + 4).
Animation: Multiply Polynomials
![Page 33: Splash Screen. Lesson 1 KC1 Lesson 1 Ex1 Simplify Expressions with Multiplication A. Simplify (–2a 3 b)(–5ab 4 ). (–2a 3 b)(–5ab 4 )= (–2 a a a b) (–5.](https://reader036.fdocuments.net/reader036/viewer/2022081602/55157f05550346a1418b557c/html5/thumbnails/33.jpg)