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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.77TI (page 1212)

Find the coefficient of the $x^{5}$ term of $(x + 4)^{8}$

Short Answer

Expert verified

Coefficient of $x^{5}$ is $3584$

Step by step solution

01

Given Information

Coefficient of the $x^{5}$ term of $(x + 4)^{8}$

02

Solution

We have

The $(r + 1)^{s t}$ term in the expansion of $(a + b)^{n}$ is

$(\begin{array}{l} n \\ r \end{array}) a^{n - r} b^{r}$

Here role="math" localid="1645254400169" $a = x, b = 4, n = 8$

$8 - r = 5 r = 3$

$(\begin{array}{l} n \\ r \end{array}) a^{n - r} b^{r} = (\begin{array}{l} 8 \\ 3 \end{array}) x^{8 - 3} 4^{3} = 56 \times 64 x^{5} = 3584 x^{5}$

Coefficient is $3584$

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Most popular questions from this chapter

Find the sum of the first 30 terms of the arithmetic sequence: 5, 9, 13, 17, 21, ….

Find the nineteenth term of a sequence where the fifth term is 1 and the common difference is −4. Give the formula for the general term.

Find the eighteenth term of a sequence where the fifth term is 12 and the common difference is seven.

In the following exercises, write the first five terms of the sequence whose general term is given.

$a_{n} = \frac{5 n - 3}{3^{n}}$

$a_{n} = {(- 1)}^{n} n^{2} .$ Write the first five terms of the sequence whose general term is

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