Q. 233 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. 233 (page 1214)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :- $x^{7}$ term of ${(x 鈭� 3)}^{9}$ .

Short Answer

Expert verified

The coefficient of $x^{7}$ is 324 .

Step by step solution

Step 1. Given Information.

Given Binomial expression is ${(x 鈥� 鈭� 鈥� 3)}^{9}$ .

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:-

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

Simplify the expression:-

$x^{9} - 27 x^{8} + 324 x^{7} - 2268 x^{6} + 10206 x^{5} - 30618 x^{4} + 61236 x^{3} - 78732 x^{2} + 59049 x - 19683$

Therefore, The coefficient of $x^{7}$ is 324 .

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91影视

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :- $x^{7}$ term of ${(x 鈭� 3)}^{9}$ .

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 coefficient of the indicated term in the expansion of the binomial :- x7term of (x鈭�3)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.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Mechanics Maths

Logic and Functions

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :- $x^{7}$ term of ${(x 鈭� 3)}^{9}$ .