NAME
DATE
10-5
PERIOD
Practice
The Binomial Theorem
Use Pascal’s triangle to expand each binomial.
1. (r + 3)5
2. (3a + b)4
r5 + 15r4 + 90r3 + 270r2
+ 405r + 243
81a4 + 108a3b + 54a2b2
+ 12ab3 + b4
Find the coefficient of the indicated term in each expansion.
3. (2n - 3m)4, 4th term
4. (4a + 2b)8, 5th term
-216
286,720
5. (3p + q)9, q5p4 term
6
) , 3rd term
6. (a - 2 √3
10,206
180
Use the Binomial Theorem to expand each binomial.
7. (x - 5)4
8. (3x + 2y)4
9. (a - √
2)
5
81x4 + 216x3y + 216x2y2 +
96xy3 + 16y4
10. (2p - 3q)6
a2
a5 - 5 √
2 a4 + 20a3 - 20 √2
2
+ 20a - 4 √
64p6 - 576p5q +
2160p4q2 - 4320p3q3 +
4860p2q4 - 2916pq5 + 729q6
11. Represent the expansion of (3x + 8y)15 using sigma notation.
15
∑
r=0
(15r ) (3x)
15 - r
(8y)r
12. SPORTS A varsity volleyball team needs nine members. Of these nine
members, at least five must be seniors. How many of the possible groups
of juniors and seniors have at least five seniors?
256
Chapter 10
28
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x4 - 20x3 + 150x2 - 500x + 625