Q. 227 In the following exercises, find... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 227 (page 1214)

In the following exercises, find the indicated term in the expansion of the binomial :- Fifth term of ${(a 鈥� + 鈥� b)}^{9}$

Short Answer

Expert verified

The fifth term of the expansion ${(a 鈥� + 鈥� b)}^{9}$ is $126 a^{5} b^{4}$ .

Step by step solution

Step 1. Given Information.

Given Binomial expression is ${(a 鈥� + 鈥� b)}^{9}$ .

Step 2. Binomial expansion formula .

The binomial expansion formula is :-

${(a + b)}^{n} = {鈭�}_{i = 0}^{n} (\binom{n}{i}) a^{(n - i)} b^{i}$

Step 3. Solve Binomial Expansion

Expanding using Binomial theorem:-

${(a 鈥� + 鈥� b)}^{9} = {鈭�}_{i = 0}^{9} (\binom{9}{i}) a^{(9 - i)} b^{i} {鈭�}_{i = 0}^{9} (\binom{9}{i}) a^{(9 - i)} b^{i} = \frac{9!}{0! (9 - 0)!} a^{9} b^{0} + \frac{9!}{1! (9 - 1)!} a^{8} b^{1} + \frac{9!}{2! (9 - 2)!} a^{7} b^{2} + \frac{9!}{3! (9 - 3)!} a^{6} b^{3} + \frac{9!}{4! (9 - 4)!} a^{5} b^{4} + \frac{9!}{5! (9 - 5)!} a^{4} b^{5} + \frac{9!}{6! (9 - 6)!} a^{3} b^{6} + \frac{9!}{7! (9 - 7)!} a^{2} b^{7} + \frac{9!}{8! (9 - 8)!} a^{1} b^{8} + \frac{9!}{9! (9 - 9)!} a^{0} b^{9}$

Simplify the expression:-

$a^{9} + 9 a^{8} b + 36 a^{7} b^{2} + 84 a^{6} b^{3} + 126 a^{5} b^{4} + 126 a^{4} b^{5} + 84 a^{3} b^{6} + 36 a^{2} b^{7} + 9 a b^{8} + b^{9}$

Therefore, The fifth term is $126 a^{5} b^{4}$ .

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91影视

In the following exercises, find the indicated term in the expansion of the binomial :- Fifth term of ${(a 鈥� + 鈥� b)}^{9}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Binomial expansion formula .

Step 3. Solve Binomial Expansion

One App. One Place for Learning.

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91影视

In the following exercises, find the indicated term in the expansion of the binomial :- Fifth term of a鈥�+鈥�b9

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Binomial expansion formula .

Step 3. Solve Binomial Expansion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term in the expansion of the binomial :- Fifth term of ${(a 鈥� + 鈥� b)}^{9}$