Q.38 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.38 (page 836)

use the Binomial Theorem to find the indicated coefficient or term.
The sixth term in the expansion of (3x +2)⁸

Short Answer

Expert verified

The sixth term is

Step by step solution

8Step 1 . Given information

Here (3x+2)⁸ is given

We have to find out the sixth term

. Expansion of (3x+2)8 using The Binomial Theorem

The binomial theorem states that

$L e t x a n d a b e r e a l n u m b e r s . F o r a n y p o s i t i v e i n t e g e r n, w e h a v e {(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + (\begin{matrix} n \\ 2 \end{matrix}) a^{2} x^{n - 2} + . . . . . . . + (\begin{matrix} n \\ j \end{matrix}) a^{j} x^{n - j} + . . . . . + (\begin{matrix} n \\ n \end{matrix}) a^{n} t h e n b a s e d b o n t h i s t h e o r e m {(3 x + 2)}^{8} b e c o m e s (3 x + 2) 8 = (\begin{matrix} 8 \\ 0 \end{matrix}) {(3 x)}^{8} + (\begin{matrix} 8 \\ 1 \end{matrix}) 脳 {(2)}^{1} {脳 (3 x)}^{8 - 1} + (\begin{matrix} 8 \\ 2 \end{matrix}) 脳 {(2)}^{2} 脳 {(3 x)}^{8 - 2} + (\begin{matrix} 8 \\ 3 \end{matrix}) 脳 {(2)}^{3} 脳 {(3 x)}^{8 - 3} + (\begin{matrix} 8 \\ 4 \end{matrix}) 脳 {(2)}^{4} 脳 {(3 x)}^{8 - 4} + (\begin{matrix} 8 \\ 5 \end{matrix}) 脳 {(2)}^{5} 脳 {(3 x)}^{8 - 5} + . . . . . + (\begin{matrix} 8 \\ 8 \end{matrix}) 脳 {(2)}^{9} = (\begin{matrix} 8 \\ 0 \end{matrix}) {(3 x)}^{8} + (\begin{matrix} 8 \\ 1 \end{matrix}) 脳 2 脳 {(3 x)}^{7} + (\begin{matrix} 8 \\ 2 \end{matrix}) 脳 4 脳 {(3 x)}^{6} + (\begin{matrix} 8 \\ 3 \end{matrix}) 脳 8 脳 {(3 x)}^{5} + (\begin{matrix} 8 \\ 4 \end{matrix}) 脳 16 脳 {(3 x)}^{4} + (\begin{matrix} 8 \\ 5 \end{matrix}) 脳 32 脳 {(3 x)}^{3} + . . . . + (\begin{matrix} 8 \\ 8 \end{matrix}) 256$

Step 3. Finding the sixth term

Based on question , sixth term from the expansion is

$(\begin{matrix} 8 \\ 5 \end{matrix}) 脳 32 脳 {(3 x)}^{3} = \frac{8!}{5! 3!} 脳 32 脳 27 脳 x^{3} = \frac{8 脳 7 脳 6 脳 5!}{3 脳 2 脳 1 脳 5!} 脳 32 脳 27 脳 x^{3} = 48384 x^{3}$

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91影视

use the Binomial Theorem to find the indicated coefficient or term.
The sixth term in the expansion of (3x +2)⁸

Short Answer

Step by step solution

8Step 1 . Given information

. Expansion of (3x+2)8 using The Binomial Theorem

Step 3. Finding the sixth term

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91影视

use the Binomial Theorem to find the indicated coefficient or term.The sixth term in the expansion of (3x +2)8

Short Answer

Step by step solution

8Step 1 . Given information

. Expansion of (3x+2)8 using The Binomial Theorem

Step 3. Finding the sixth term

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

use the Binomial Theorem to find the indicated coefficient or term.
The sixth term in the expansion of (3x +2)⁸