Ms. DePalma's Math World - Home
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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