Q.37 use the Binomial Theorem to find... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q.37 (page 836)

use the Binomial Theorem to find the indicated coefficient or term.
The third term in the expansion of (3x - 2)⁹

Short Answer

Expert verified

The third term is $314928 x^{7}$

Step by step solution

. Given information

In this question (3x-2)⁹ is given.

We have to find out the third term

. Expansion of (3x-2)9 using The Binomial Theorem

According to the binomial theorem

$L e t x a n d a b e r e a l n u m b e r s . F o r a n y p o s i t i v e i n t e g e r n, w e h a v e {(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + (\begin{matrix} n \\ 2 \end{matrix}) a^{2} x^{n - 2} + . . . . . . . + (\begin{matrix} n \\ j \end{matrix}) a^{j} x^{n - j} + . . . . . + (\begin{matrix} n \\ n \end{matrix}) a^{n}$

So given expression becomes

${(3 x - 2)}^{9} = (\begin{matrix} 9 \\ 0 \end{matrix}) {(3 x)}^{9} + (\begin{matrix} 9 \\ 1 \end{matrix}) 脳 {(- 2)}^{1} {脳 (3 x)}^{9 - 1} + (\begin{matrix} 9 \\ 2 \end{matrix}) 脳 {(- 2)}^{2} 脳 {(3 x)}^{9 - 2} + . . . . . + (\begin{matrix} 9 \\ 8 \end{matrix}) 脳 {(- 2)}^{8} {脳 (3 x)}^{9 - 8} + (\begin{matrix} 9 \\ 9 \end{matrix}) 脳 {(- 2)}^{9} = (\begin{matrix} 9 \\ 0 \end{matrix}) {(3 x)}^{9} - (\begin{matrix} 9 \\ 1 \end{matrix}) 脳 2 脳 {(3 x)}^{8} + (\begin{matrix} 9 \\ 2 \end{matrix}) 脳 4 脳 {(3 x)}^{7} + . . . . + (\begin{matrix} 9 \\ 8 \end{matrix}) 256 (3 x) - (\begin{matrix} 9 \\ 9 \end{matrix}) 512$

Step 3. Description of finding the third term

The third term from the expanded form of the given expression is

$(\begin{matrix} 9 \\ 2 \end{matrix}) 脳 4 脳 {(3 x)}^{7} = \frac{9!}{2! 7!} 脳 4 脳 3^{7} 脳 x^{7} = \frac{9 脳 8 脳 7!}{1 脳 2 脳 7!} 脳 4 脳 3^{7} 脳 x^{7} = 314928 x^{7}$

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91影视

use the Binomial Theorem to find the indicated coefficient or term.
The third term in the expansion of (3x - 2)⁹

Short Answer

Step by step solution

. Given information

. Expansion of (3x-2)9 using The Binomial Theorem

Step 3. Description of finding the third term

One App. One Place for Learning.

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91影视

use the Binomial Theorem to find the indicated coefficient or term. The third term in the expansion of (3x - 2)9

Short Answer

Step by step solution

. Given information

. Expansion of (3x-2)9 using The Binomial Theorem

Step 3. Description of finding the third term

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Applied Mathematics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

use the Binomial Theorem to find the indicated coefficient or term.
The third term in the expansion of (3x - 2)⁹