Chapter 12: Q. 318 (page 1221)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $x^{5}$ term of ${(x - 2)}^{8}$ .

Short Answer

Expert verified

The coefficient of $x^{5}$ term in the expansion of ${(x - 2)}^{8}$ is $- 448$ .

Step by step solution

Step 1. Given

A binomial is given as ${(x - 2)}^{8}$ .

To find the coefficient of the term $x^{5}$ in the expansion of the given binomial.

Step 2. Compare binomial (a+b)n and (x-2)8.

On Comparing, we get

$a = x b = - 2 n = 8$

Now in the formula ${}^{n}C_{r} a^{n - r} b^{r}$ ,

$n - r = 5 8 - r = 5 r = 3$

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

This gives

${}^{8}C_{3} y^{8 - 3} {(- 2)}^{3} = \frac{8!}{(8 - 3)! 3!} y^{5} {(- 2)}^{3} = - 8 y^{5} \frac{8!}{5! 3!} = - 8 y^{5} (56) = - 448 y^{5}$

The coefficient of $y^{5}$ for ${(y - 2)}^{8}$ is $- 448$ .

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In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $x^{5}$ term of ${(x - 2)}^{8}$ .

Short Answer

Step by step solution

Step 1. Given

Step 2. Compare binomial (a+b)n and (x-2)8.

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

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In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :x5term of(x-2)8.

Short Answer

Step by step solution

Step 1. Given

Step 2. Compare binomial (a+b)n and (x-2)8.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $x^{5}$ term of ${(x - 2)}^{8}$ .