Q. 228 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. 228 (page 1214)

In the following exercises, find the indicated term in the expansion of the binomial :- Fourth term of ${(x 鈥� 鈭� 鈥� y)}^{8}$

Short Answer

Expert verified

Fourth term of the expansion ${(x 鈥� 鈭� 鈥� y)}^{8}$ is $- 56 x^{5} y^{3}$ .Step 1. Given Information.

Step by step solution

Step 1. Given Information.

Given Binomial expression is ${(x 鈥� 鈭� 鈥� y)}^{8}$ .

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:-

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

Simplify the expression:-

$x^{8} - 8 x^{7} y + 28 x^{6} y^{2} - 56 x^{5} y^{3} + 70 x^{4} y^{4} - 56 x^{3} y^{5} + 28 x^{2} y^{6} - 8 x y^{7} + y^{8}$

Therefore, The fourth term is $- 56 x^{5} y^{3}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, find the indicated term in the expansion of the binomial :- Fourth term of ${(x 鈥� 鈭� 鈥� y)}^{8}$

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

Logic and Functions

Mechanics Maths

Discrete Mathematics

Calculus

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, find the indicated term in the expansion of the binomial :- Fourth term of x鈥�鈭�鈥�y8

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

Logic and Functions

Mechanics Maths

Discrete Mathematics

Calculus

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term in the expansion of the binomial :- Fourth term of ${(x 鈥� 鈭� 鈥� y)}^{8}$