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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 235 (page 1214)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial.
$p^{5} q^{4} term of {(3 p + q)}^{9}$

Short Answer

Expert verified

The coefficient of $p^{5} q^{4}$ term in the expansion of ${(3 p + q)}^{9}$ is 30,618.

Step by step solution

01

Step 1. Given information.

Find the coefficient of the indicated term in the expansion of the binomial.

$p^{5} q^{4} term of {(3 p + q)}^{9}$

02

Step 2. Compare binomial (a+b)n and 3p+q9.

On comparing we get,

$a = 3 p b = q n = 9$

Now in the formula

$n - r = 5 9 - r = 5 r = 4$

03

Step 3. Substitute the obtained values in the formula Crnan-rbr.

${}^{9}C_{4} {(3 p)}^{9 - 4} q^{4} = \frac{9! 鈥�}{(9 - 4)! 鈥� 4! 鈥�} (243 p^{5}) q^{4} = \frac{9 路 8 路 7 路 6 路 5! 鈥�}{5! 鈥� 路 4 路 3 路 2 路 1} (243 p^{5}) q^{4} = 126 路 (243 p^{5}) q^{4} = 30618$

04

Step 4. conclusion.

The coefficient of $p^{5} q^{4}$ term in the expansion of ${(3 p + q)}^{9}$ is 30,618.

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Most popular questions from this chapter

In the following exercises, expand each binomial using Pascal's Triangle.

$(a - b)^{6}$

Write the first five terms of the sequence whose general term is $a_{n} = \frac{2}{n!} .$

In the following exercises, evaluate.

(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

Determine if each sequence is geometric. If so indicate the common ratio.

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鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

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