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

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

Coefficient is $280$

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

Short Answer

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

Short Answer

Step by step solution

Given Information

Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Statistics

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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