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Lesson 1 KC1

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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 a b b b b) Definition of exponents = –2(–5) a a a a b b b b b Commutative Property =10a 4 b 5 Definition of exponents Answer:10a 4 b 5

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Lesson 1 Ex1 Simplify Expressions with Multiplication B. Simplify (3a 5 )(c –2 )(–2a –4 b 3 ). (3a 5 )(c –2 )(–2a –4 b 3 ) Definition of negative exponents Definition of exponents

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Lesson 1 Ex1 Simplify Expressions with Multiplication Cancel out common factors. Definition of exponents and fractions Answer:

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A.A B.B C.C D.D Lesson 1 CYP1 A. Simplify (–3x 2 y)(5x 3 y 5 ). A.–15x 5 y 6 B.–15x 6 y 5 C.15x 5 y 6 D.

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A.A B.B C.C D.D Lesson 1 CYP1 B. Simplify (4x –2 )(xy –3 ). A. B. C. D.

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Lesson 1 KC2

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Lesson 1 KC3

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Lesson 1 Ex2 Simplify Expressions with Division Answer: Remember that a simplified expression cannot contain negative exponents. Subtract exponents.

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Lesson 1 CYP2 1.A 2.B 3.C 4.D A.x 10 B.x 21 C.x 4 D.

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Lesson 1 KC4

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Lesson 1 Ex3 Simplify Expressions with Powers A. Simplify (–3c 2 d 5 ) 3. (–3c 2 d 5 ) 3 =(–3) 3 (c 2 ) 3 (d 5 ) 3 Power of a power =–27c 6 d 15 Simplify. Answer: –27c 6 d 15

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Lesson 1 Ex3 Simplify Expressions with Powers Power of a product Power of a quotient B. (–2) 5 = –32 Answer:

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1.A 2.B 3.C 4.D Lesson 1 CYP3 A. Simplify (x 3 ) 5. A.x 15 B.x 8 C.x 2 D.

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1.A 2.B 3.C 4.D Lesson 1 CYP3 B. Simplify. A. B. C. D.

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Lesson 1 Ex4 Method 1Raise the numerator and the denominator to the fifth power before simplifying. Simplify Expressions Using Several Properties

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Lesson 1 Ex4 Simplify Expressions Using Several Properties Answer:

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Lesson 1 Ex4 Method 2Simplify the fraction before raising to the fifth power. Simplify Expressions Using Several Properties

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Lesson 1 Ex4 Simplify Expressions Using Several Properties Answer:

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A.A B.B C.C D.D Lesson 1 CYP4 A. B. C. D.

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Lesson 1 Ex5 BIOLOGY There are about 5 × 10 6 red blood cells in one milliliter of blood. A certain blood sample contains 8.32 × 10 6 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

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A.A B.B C.C D.D Lesson 1 CYP5 A.2 B.20 C.2 × 10 2 D × BIOLOGY A petri dish started with 3.6 × 10 5 germs in it. A half hour later, there are 7.2 × How many times as great is the amount a half hour later?

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End of Lesson 1

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Lesson 2 Ex2 Simplify Polynomials A. Simplify (2a 3 + 5a – 7) – (a 3 – 3a + 2). (2a 3 + 5a – 7) – (a 3 – 3a + 2) = a 3 + 8a – 9Combine like terms. Group like terms. Distribute the –1. Answer: a 3 + 8a – 9

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Lesson 2 Ex2 Simplify Polynomials B. Simplify (4x 2 – 9x + 3) + (–2x 2 – 5x – 6). (4x 2 – 9x + 3) + (–2x 2 – 5x – 6) = 2x 2 – 14x – 3Combine like terms. Remove parentheses. Group like terms. Answer: 2x 2 – 14x – 3

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Lesson 2 CYP2 1.A 2.B 3.C 4.D A.7x 2 + 3x – 8 B.–x 2 + 3x – 8 C.–x 2 + 3x + 2 D.–x 2 + x + 2 A. Simplify (3x 2 + 2x – 3) – (4x 2 + x – 5).

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Lesson 2 CYP2 1.A 2.B 3.C 4.D A.9x 2 + 6x + 7 B.–7x 2 – 5x + 6 C.3x 2 – 6x + 7 D.3x 2 – 2x + 6 B. Simplify (–3x 2 – 4x + 1) – (4x 2 + x – 5).

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Lesson 2 Ex3 Simplify Using the Distributive Property Find –y(4y 2 + 2y – 3). –y(4y 2 + 2y – 3) = –y(4y 2 ) –y(2y) – y(–3) Distributive Property = –4y 3 – 2y 2 + 3y Multiply the monomials. Answer: –4y 3 – 2y 2 + 3y

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1.A 2.B 3.C 4.D Lesson 2 CYP3 A.–3x 2 – 2x + 5 B.–4x 4 – 3x 2 – 6x C.–3x 4 + 2x 2 – 5x D.–3x 4 – 2x 3 + 5x Find –x(2x 3 – 2x + 5).

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Lesson 2 Ex4 Find (a 2 + 3a – 4)(a + 2). (a 2 + 3a – 4)(a + 2) = a 3 + 5a 2 + 2a – 8Combine like terms. Multiply Polynomials Distributive Property Multiply monomials. Answer: a 3 + 5a 2 + 2a – 8

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A.A B.B C.C D.D Lesson 2 CYP4 A.x 3 + 7x x – 8 B.x 2 + 4x + 2 C.x 3 + 3x 2 – 2x + 8 D.x 3 + 7x x – 8 Find (x 2 + 3x – 2)(x + 4). Animation: Multiply Polynomials

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End of Lesson 2

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