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The Binomial Theorem

Practice and Problem Solving: A/B

Use the Binomial Theorem to expand each binomial.

1. (x + y)3

2. (2x + y)4

3. (m + 3n)3

4. (p + q)5

5. (4x + y)4

6. (2x + y)5

1. x2; 4; 2x3 + 8x

2. 2; m3; 6m − 3m4

3. 6p2 + 42p

4. x3 + 3x2 − x

5. 4x3 − 10x2 + 12x

6. a. −3x2

b. −6x

c. 3

d. −3x2 − 6x + 3

e. x3 − x2 − 7x + 3

7. x2; 3x; −2; x2; 3x; −2; x3 + 2x2 − 5x + 2

8. x + 3; x + 3; x2 + 6x + 9;

x3 + 9x2 + 27x + 27

9. x − 5; x − 5; x2 − 10x + 25;

x3 − 15x2 + 75x − 125

10. 3wd−4d

Reading Strategies

1. Yes; 3x2

2. No; 2x2 + x − 3

3. a. 6x4 + 3x3 − 9x2

b. 3

c. 4

4. Possible answer: Add the exponents. xm(xn) ’ xm + n

Success for English Learners

1. Use arrows to keep track of products.

2. Possible answer:

[pic]

[pic]

LESSON 6-3

Practice and Problem Solving: A/B

1. x3 + 3x2y + 3xy2 + y3

2. 16x4 + 32x3y + 24x2y2 + 8xy3 + y4

3. m3 + 9m2n + 27mn2 + 27n3

4. p5 + 5p4q + 10p3q2 + 10p2q3 + 5pq4 + q5

5. a. 0.015

b. 0.13

6. a. 0.004

b. 0.33

7. 0.17

8. 0.65

Practice and Problem Solving: C

1. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5

2. 256x4 + 256x3y + 96x2y2 + 16xy3 + y4

3. 32x5 + 80x4y + 80x3y2 + 40x2y3 + 10xy4 +y5

4. 16m4 + 32m3n + 24m2n2 + 8mn3 + n4

5. a. 0.09

b. 0.01

6. a. 0.01

b. 0.08

7. 0.15

8. 0.01

Practice and Problem Solving: Modified

1. x2 + 2xy + y2

2. a3 + 3a2b + 3ab2 + b3

3. 4x2 + 4xy + y2

4. x3 + 9x2y + 27xy2 + 27y3

5. a. 0.5

b. 0.5

c. 0.31

d. 0.47

6. a. 0.40

b. 0.10

c. 0.41

d. 0.11

Reading Strategies

1. a. n ’ 2, [pic], [pic], [pic]

b. [pic]; [pic]

c. [pic]

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lesson

6-3

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