## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Tip our Team

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

## Holooly Tables

All the data tables that you may search for.

## Holooly Help Desk

Need Help? We got you covered.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

## Q. 10.5.4

Finding a Single Term of a Binomial Expansion

Find the fourth term in the expansion of $(3 x+2 y)^7$.

## Verified Solution

We are looking for the fourth term. The value of r is one less than the term to be found. Thus, r = 3. In the expansion of $(3 x+2 y)^7$, a = 3x, b = 2y, and n = 7.

The fourth term is Now we need to evaluate the factorial expression and raise 3x and 2y to the indicated powers. We obtain

$\frac{7 !}{3 ! 4 !}\left(81 x^4\right)\left(8 y^3\right)=\frac{7 \cdot 6 \cdot 5 \cdot \cancel{4 !}}{3 \cdot 2 \cdot 1 \cdot \cancel{4 !}}\left(81 x^4\right)\left(8 y^3\right)=35\left(81 x^4\right)\left(8 y^3\right)=22,680 x^4 y^3$.

The fourth term of $(3 x+2 y)^7$ is $22,680 x^4 y^3$.