Q. 229 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. 229 (page 1214)

In the following exercises, find the indicated term in the expansion of the binomial :- Seventh term of ${(x 鈭� y)}^{11}$ .

Short Answer

Expert verified

The seventh term of the expansion is $462 x^{5} y^{6}$ .

Step by step solution

Step 1. Given Information.

Given Binomial expression is ${(x 鈥� 鈭� 鈥� y)}^{11}$ .

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:-

${(x 鈥� 鈭� 鈥� y)}^{11} = {鈭�}_{i = 0}^{11} (\binom{11}{i}) x^{(11 - i)} {(- y)}^{i} {鈭�}_{i = 0}^{11} (\binom{11}{i}) x^{(11 - i)} {(- y)}^{i} = \frac{11!}{0! (11 - 0)!} x^{11} {(- y)}^{0} + \frac{11!}{1! (11 - 1)!} x^{10} {(- y)}^{1} + \frac{11!}{2! (11 - 2)!} x^{9} {(- y)}^{2} + \frac{11!}{3! (11 - 3)!} x^{8} {(- y)}^{3} + \frac{11!}{4! (11 - 4)!} x^{7} {(- y)}^{4} + \frac{11!}{5! (11 - 5)!} x^{6} {(- y)}^{5} + \frac{11!}{6! (11 - 6)!} x^{5} {(- y)}^{6} + \frac{11!}{7! (11 - 7)!} x^{4} {(- y)}^{7} + \frac{11!}{8! (11 - 8)!} x^{3} {(- y)}^{8} + \frac{11!}{9! (11 - 9)!} x^{2} {(- y)}^{9} + \frac{11!}{10! (11 - 10)!} x^{1} {(- y)}^{10} + \frac{11!}{11! (11 - 11)!} x^{0} {(- y)}^{11}$

Simplify the expression:-

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} - y^{11}$

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91影视

In the following exercises, find the indicated term in the expansion of the binomial :- Seventh term of ${(x 鈭� y)}^{11}$ .

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 :- Seventh term of (x鈭�y)11.

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

Calculus

Pure Maths

Geometry

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term in the expansion of the binomial :- Seventh term of ${(x 鈭� y)}^{11}$ .