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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.76TI (page 1211)

Find the fifth term of $(a + b)^{8}$

Short Answer

Expert verified

Fifth term is $70 a^{4} b^{4}$

Step by step solution

01

Given Information

Fifth term of $(a + b)^{8}$

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

$r + 1 = 5 r = 4 n = 8 (\begin{array}{l} n \\ r \end{array}) a^{n - r} b^{r} = (\begin{array}{l} 8 \\ 4 \end{array}) a^{8 - 4} b^{4} = 70 a^{4} b^{4}$

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Most popular questions from this chapter

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = 4$ and $r = 3$

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

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