splash screen. lesson 1 kc1 lesson 1 ex1 simplify expressions with multiplication a. simplify (–2a...

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

Simplify Expressions with Multiplication

B. Simplify (3a5)(c–2)(–2a–4b3).

(3a5)(c–2)(–2a–4b3)

Definition of negative exponents

Definition of exponents

Simplify Expressions with Multiplication

Cancel out common factors.

Definition of exponents and fractions

Answer:

A. A

B. B

C. C

D. D

0% 0%0%0%

A. Simplify (–3x2y)(5x3y5).

A. –15x5y6

B. –15x6y5

C. 15x5y6

D.

A. A

B. B

C. C

D. D

0% 0%0%0%

B. Simplify (4x–2)(xy–3).

A.

B.

C.

D.

Simplify Expressions with Division

Answer:

Remember that a simplified expression cannot contain negative exponents.

Subtract exponents.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. x10

B. x21

C. x4

D.

Simplify Expressions with Powers

A. Simplify (–3c2d5)3.

(–3c2d5)3 = (–3)3(c2)3(d5)3 Power of a power

= –27c6d15 Simplify.

Answer: –27c6d15

Simplify Expressions with Powers

Power of a product

Power of a quotient

B.

(–2)5 = –32

Answer:

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. Simplify (x3)5.

A. x15

B. x8

C. x2

D.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

B. Simplify .

A.

B.

C.

D.

Method 1 Raise the numerator and the denominator to the fifth power before simplifying.

Simplify Expressions Using Several Properties

Simplify Expressions Using Several Properties

Answer:

Method 2 Simplify the fraction before raising to the fifth power.

Simplify Expressions Using Several Properties

Simplify Expressions Using Several Properties

Answer:

A. A

B. B

C. C

D. D

0% 0%0%0%

A.

B.

C.

D.

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

A. A

B. B

C. C

D. D

0% 0%0%0%

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?

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

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

1. A

2. B

3. C

4. D

0%0%0%0%

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).

1. A

2. B

3. C

4. D

0%0%0%0%

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).

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

1. A

2. B

3. C

4. D

0%0%0%0%

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).

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

A. A

B. B

C. C

D. D

0% 0%0%0%

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