Chapter 12: Q36. (page 637)

Find the indicated term of each expansion.
Fifth term of ${(2 a - b)}^{7}$

Short Answer

Expert verified

The fifth term of the expansion is $T_{5} = 280 a^{3} b^{4}$ .

Step by step solution

Step 1. Given Information.

Given, binomial expansion is ${(2 a - b)}^{7}$ and the fifth term of the expansion is to be determined.

Step 2. Calculation.

The general term of the binomial expansion ${(x + y)}^{n}$ is given by:

$T_{r + 1} = \frac{n!}{(n - r)! r!} x^{n - r} y^{r}$

Here n=7, x = 2a, y = -b and r + 1 = 5.

Plugging the values:

$\begin{array}{l} T_{r + 1} = \frac{n!}{(n - r)! r!} x^{n - r} y^{r} \\ T_{5} = \frac{7!}{(7 - 4)! 4!} {(2 a)}^{7 - 4} {(- b)}^{4} \\ T_{5} = \frac{7!}{3! 4!} {(2 a)}^{3} b^{4} \\ T_{5} = 280 a^{3} b^{4} \end{array}$

Step 3. Conclusion.

Hence, the third term of the expansion is $T_{5} = 280 a^{3} b^{4}$ .

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Find the indicated term of each expansion.
Fifth term of ${(2 a - b)}^{7}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the indicated term of each expansion.Fifth term of 2a-b7

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Find the indicated term of each expansion.
Fifth term of ${(2 a - b)}^{7}$