Q.35 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.35 (page 836)

use the Binomial Theorem to find the indicated coefficient or term.
The fifth term in the expansion of (x + 3)⁷

Short Answer

Expert verified

The fifth term is 2835 x³

Step by step solution

. Given information

In this question (x+3)⁷ is given

We have to find out the fifth term

. Expansion of (x+3)7 using The Binomial Theorem

According to the binomial theorem

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

based on this theorem, the expanded form of (x+3)⁷ is

localid="1647340067248" ${(x + 3)}^{7} = (\begin{matrix} 7 \\ 0 \end{matrix}) x^{7} + (\begin{matrix} 7 \\ 1 \end{matrix}) 脳 3^{1} {脳 x}^{7 - 1} + (\begin{matrix} 7 \\ 2 \end{matrix}) 脳 3^{2} 脳 x^{7 - 2} + (\begin{matrix} 7 \\ 3 \end{matrix}) 脳 3^{3} 脳 x^{7 - 3} + (\begin{matrix} 7 \\ 4 \end{matrix}) 脳 3^{4} x^{7 - 4} . . . . . . + (\begin{matrix} 7 \\ 6 \end{matrix}) 脳 3^{6} {脳 (2 x)}^{9 - 8} + (\begin{matrix} 7 \\ 7 \end{matrix}) 脳 3^{7} = (\begin{matrix} 7 \\ 0 \end{matrix}) x^{7} + (\begin{matrix} 7 \\ 1 \end{matrix}) 3 x^{6} + (\begin{matrix} 9 \\ 2 \end{matrix}) 9 x^{5} + (\begin{matrix} 9 \\ 3 \end{matrix}) 27 x^{6} + (\begin{matrix} 7 \\ 4 \end{matrix}) 81 x^{3} . . . . . . + (\begin{matrix} 7 \\ 6 \end{matrix}) 729 x + (\begin{matrix} 7 \\ 7 \end{matrix}) 2187$

Step 3. Description of finding the fifth term

the fifth term from the expanded form is

(\begin{matrix} 7 \\ 4 \end{matrix}) 81 x^{3} = \frac{7!}{3! 4!} 脳 81 脳 x^{3} = \frac{7 脳 6 脳 5 脳 4!}{3 脳 2 脳 1 脳 4!} 脳 81 脳 x^{3} = 2835 x^{3}

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91影视

use the Binomial Theorem to find the indicated coefficient or term.
The fifth term in the expansion of (x + 3)⁷

Short Answer

Step by step solution

. Given information

. Expansion of (x+3)7 using The Binomial Theorem

Step 3. Description of finding the fifth 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 fifth term in the expansion of (x + 3)7

Short Answer

Step by step solution

. Given information

. Expansion of (x+3)7 using The Binomial Theorem

Step 3. Description of finding the fifth term

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Mechanics Maths

Logic and Functions

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

use the Binomial Theorem to find the indicated coefficient or term.
The fifth term in the expansion of (x + 3)⁷