Chapter 12: Q. 319 (page 1221)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $a^{3} b^{4}$ term of ${(2 a + b)}^{7}$ .

Short Answer

Expert verified

The coefficient of $a^{3} b^{4}$ term in the expansion of ${(2 a + b)}^{7}$ is $280$ .

Step by step solution

Step 1. Given

A binomial is given as ${(2 a + b)}^{7}$ .

To find the coefficient of the term $a^{3} b^{4}$ in the expansion of the given binomial.

Step 2. Compare binomial (a+b)n and (2a+b)7.

On Comparing, we get

$a = 2 a b = b n = 7$

Now in the formula ,

$n - r = 3 7 - r = 3 r = 4$

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

We get

${}^{7}C_{4} {(2 a)}^{7 - 4} b^{4} = \frac{7!}{(7 - 4)! 4!} (8 a^{3}) b^{4} = 35 (8 a^{3}) b^{4} = 280 a^{3} b^{4}$

The coefficient of the term $a^{3} b^{4}$ for the given binomial is $280$ .

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In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $a^{3} b^{4}$ term of ${(2 a + b)}^{7}$ .

Short Answer

Step by step solution

Step 1. Given

Step 2. Compare binomial (a+b)n and (2a+b)7.

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 :a3b4term of(2a+b)7.

Short Answer

Step by step solution

Step 1. Given

Step 2. Compare binomial (a+b)n and (2a+b)7.

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

Discrete Mathematics

Applied Mathematics

Calculus

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Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : $a^{3} b^{4}$ term of ${(2 a + b)}^{7}$ .