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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. 12.78TI (page 1212)

Find the coefficient of the $x^{4}$ term of $(x + 2)^{7}$ .

Short Answer

Expert verified

Coefficient of the $x^{4}$ term is $280$

Step by step solution

Given Information

Coefficient of the $x^{4}$ term of $(x + 2)^{7}$ .

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 $a = x, b = 2, n = 7$

$n - r = 4 7 - r = 4 r = 3 (\begin{array}{l} n \\ r \end{array}) a^{n - r} b^{r} = (\begin{array}{l} 7 \\ 3 \end{array}) x^{7 - 3} 2^{3} = 35 脳 8 x^{4} = 280 x^{4}$

Coefficient is $280$

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Find the coefficient of the x4 term of (x+2)7.

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Find the coefficient of the $x^{4}$ term of $(x + 2)^{7}$ .