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2 3 1 3
Answers to Math
Applications
Math Applications for this
chapter are on pages 422–429.
The notes and solutions shown
below accompany the suggested
applications to assign with this
lesson.
1. a. 28 – 21 = 7
28 + 7 + 1 = 36
b. Calculate the difference
between the last two terms
and then add 1. Add the
result to the last term in
the sequence to find the
next term in the sequence.
c. n 3
= (n 2
– n 1
+ 1) + n 2
=
2n 2
– n 1
+ 1
2. a. 2 0 , 2 1 , 2 2 , and 2 3
b. Let the row number
equal n.
n – 1 = 8
n = 9 or 9th row
c. 2 8 = 1 + 8 + 28 + 56
+ 70 + 56 + 28 + 8 + 1
= 256
Extra Practice 9.5 (CRB)
NAME CLASS DATE
EXTRA PRACTICE 11.5 THE BINOMIAL THEOREM
Use Pascal’s Triangle to expand each binomial.
1. (y – z) 2 2. (m + n) 4
y 2 – 2yz + z 2 m 4 + 4m 3 n + 6m 2 n 2 + 4mn 3 + n 4
3. (a – b) 3 4. (x + y) 5
a 3 – 3a 2 b + 3ab 2 – b 3 x 5 + 5x 4 y + 10x 3 y 2 + 10x 2 y 3 + 5xy 4 + y 5
5. (c – d) 5 6. (w + 1) 4
c 5 – 5c 4 d + 10c 3 d 2 – 10c 2 d 3 + 5cd 4 – d 5 w 4 + 4w 3 + 6w 2 + 4w + 1
7. (m – 2) 6 m 6 – 12m 5 + 60m 4 – 160m 3 + 240m 2 – 192m + 64
Use the Binomial Theorem to expand each binomial.
8. (x + y) 4 9. (a + 2b) 4
x 4 + 4x 3 y + 6x 2 y 2 + 4xy 3 + y 4 a 4 + 8a 3 b + 24a 2 b 2 + 32ab 3 + 16b 4
10. (a + 3b) 4 11. (n – 1) 5
a 4 + 12a 3 b + 54a 2 b 2 + 108ab 3 + 81b 4 n 5 – 5n 4 + 10n 3 – 10n 2 + 5nd 4 – 1
12. (t – 1) 6 13. (3a + b) 4
t 6 – 6t 5 + 15t 4 – 20t 3 + 15t 2 – 6t + 1 81a 4 + 108a 3 b + 54a 2 b 2 + 12ab 3 + b 4
14. (x – 3y) 5 x 5 – 15x 4 y + 90x 3 y 2 – 270x 2 y 3 + 405xy 4 – 243y 5
Find the specified term of each binomial expansion.
15. the fourth term of (x + y) 8 16. the seventh term of (a + b) 11
56x 5 y 3 462a 5 b 6
17. the fifth term of (c – d) 9 18. the fourth term of (m – 2n) 6
126c 5 d 4 –160m 3 n 3
19. the third term of (2y – 5z) 5 20. the eighth term of (a + b) 20
2,000y 3 z 2 77,520a 13 b 7
328 >Algebra 2 Chapter Resource Book
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9.5 The Binomial Theorem 419